Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Factorization - Exercise 7.5
Factorization - Exercise 7.5 | Mathematics (Maths) Class 8 PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Q u e s t i o n : 7 4
Factorize each of the following expression:
16x
2
- 25y
2
S o l u t i o n :
16x
2
-25y
2
= 4x)
2
- 5y)
2
= 4x -5y 4x +5y
Q u e s t i o n : 7 5
Factorize each of the following expression:
27x
2
- 12y
2
S o l u t i o n :
27x
2
-12y
2
= 3 9x
2
-4y
2
= 3 3x)
2
- 2y)
2
= 3 3x -2y 3x +2y
Q u e s t i o n : 7 6
Factorize each of the following expression:
144a
2
- 289b
2
S o l u t i o n :
144a
2
-289b
2
= 12a)
2
- 17b)
2
= 12a -17b 12a +17b
Q u e s t i o n : 7 7
Factorize each of the following expression:
12m
2
- 27
S o l u t i o n :
12m
2
-27 = 3 4m
2
-9 = 3 2m)
2
-3
2
= 3 2m -3 2m +3
Q u e s t i o n : 7 8
Factorize each of the following expression:
125x
2
- 45y
2
S o l u t i o n :
125x
2
-45y
2
= 5 25x
2
-9y
2
= 5 5x)
2
- 3y)
2
= 5 5x -3y 5x +3y
Q u e s t i o n : 7 9
Factorize each of the following expression:
144a
2
- 169b
2
S o l u t i o n :
144a
2
-169b
2
= 12a)
2
- 13b)
2
= 12a -13b 12a +13b
Q u e s t i o n : 8 0
Factorize each of the following expression:
(2a - b)
2
- 16c
2
S o l u t i o n :
2a -b)
2
-16c
2
= 2a -b)
2
- 4c)
2
= 2a -b -4c 2a -b +4c = 2a -b -4c 2a -b +4c
Q u e s t i o n : 8 1
Factorize each of the following expression:
(x + 2y)
2
- 4(2x - y)
2
( ( ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ) [( ] ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( )
Page 2
Q u e s t i o n : 7 4
Factorize each of the following expression:
16x
2
- 25y
2
S o l u t i o n :
16x
2
-25y
2
= 4x)
2
- 5y)
2
= 4x -5y 4x +5y
Q u e s t i o n : 7 5
Factorize each of the following expression:
27x
2
- 12y
2
S o l u t i o n :
27x
2
-12y
2
= 3 9x
2
-4y
2
= 3 3x)
2
- 2y)
2
= 3 3x -2y 3x +2y
Q u e s t i o n : 7 6
Factorize each of the following expression:
144a
2
- 289b
2
S o l u t i o n :
144a
2
-289b
2
= 12a)
2
- 17b)
2
= 12a -17b 12a +17b
Q u e s t i o n : 7 7
Factorize each of the following expression:
12m
2
- 27
S o l u t i o n :
12m
2
-27 = 3 4m
2
-9 = 3 2m)
2
-3
2
= 3 2m -3 2m +3
Q u e s t i o n : 7 8
Factorize each of the following expression:
125x
2
- 45y
2
S o l u t i o n :
125x
2
-45y
2
= 5 25x
2
-9y
2
= 5 5x)
2
- 3y)
2
= 5 5x -3y 5x +3y
Q u e s t i o n : 7 9
Factorize each of the following expression:
144a
2
- 169b
2
S o l u t i o n :
144a
2
-169b
2
= 12a)
2
- 13b)
2
= 12a -13b 12a +13b
Q u e s t i o n : 8 0
Factorize each of the following expression:
(2a - b)
2
- 16c
2
S o l u t i o n :
2a -b)
2
-16c
2
= 2a -b)
2
- 4c)
2
= 2a -b -4c 2a -b +4c = 2a -b -4c 2a -b +4c
Q u e s t i o n : 8 1
Factorize each of the following expression:
(x + 2y)
2
- 4(2x - y)
2
( ( ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ) [( ] ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( )
S o l u t i o n :
x +2y)
2
-4 2x -y)
2
= x +2y)
2
- 2 2x -y ]
2
= x +2y -2 2x -y x +2y +2 2x -y = x +2y -4x +2y x +2y +4x -2y =
Q u e s t i o n : 8 2
Factorize each of the following expression:
3a
5
- 48a
3
S o l u t i o n :
3a
5
-48a
3
= 3a
3
a
2
-16 = 3a
3
a
2
-4
2
= 3a
3
a -4 a +4
Q u e s t i o n : 8 3
Factorize each of the following expression:
a
4
- 16b
4
S o l u t i o n :
a
4
-16b
4
= a
4
-2
4
b
4
= a
2
)
2
- 2
2
b
2
)
2
= a
2
-2
2
b
2
a
2
+2
2
b
2
= a
2
- 2b)
2
a
2
+4b
2
= a -2b a +2b a
2
+4b
2
Q u e s t i o n : 8 4
Factorize each of the following expression:
x
8
- 1
S o l u t i o n :
x
8
-1 = x
4
)
2
-1
2
= x
4
-1 x
4
+1 = x
2
)
2
-1
2
x
4
+1 = x
2
-1 x
2
+1 x
4
+1 = x
2
-1
2
x
2
+1 x
4
+1 = x -1 x +1 x
2
+1 x
4
+1
Q u e s t i o n : 8 5
Factorize each of the following expression:
64 - (a + 1)
2
S o l u t i o n :
64 - a +1)
2
= 8)
2
- a +1)
2
= 8 - a +1 8 + a +1 = 8 -a -1 8 +a +1 = 7 -a 9 +a
Q u e s t i o n : 8 6
Factorize each of the following expression:
36l
2
- (m + n)
2
S o l u t i o n :
36l
2
- m +n)
2
= 6l)
2
- m +n)
2
= 6l - m +n 6l + m +n = 6l -m -n 6l +m +n
Q u e s t i o n : 8 7
Factorize each of the following expression:
25x
4
y
4
- 1
S o l u t i o n :
25x
4
y
4
-1 = 5x
2
y
2
)
2
-1 = 5x
2
y
2
-1 5x
2
y
2
+1
Q u e s t i o n : 8 8
Factorize each of the following expression:
a
4
-
1
b
4
S o l u t i o n :
a
4
- 1/b
4
= (a
2
)
2
- 1/(b
2
)
2
= a
2
- 1/b
2
a
2
+ 1/b
2
= a - 1/ba + 1/ba
2
+ 1/b
2
Q u e s t i o n : 8 9
Factorize each of the following expression:
x
3
- 144x
S o l u t i o n :
x
3
-144x = x x
2
-144 = x x
2
-12
2
= x x -12 x +12
Q u e s t i o n : 9 0
Factorize each of the following expression:
(x - 4y)
2
- 625
S o l u t i o n :
x -4y)
2
-625 = x -4y)
2
-25
2
= x -4y -25 x -4y +25 = x -4y -25 x -4y +25
Q u e s t i o n : 9 1
Factorize each of the following expression:
9(a - b)
2
- 100(x - y)
2
S o l u t i o n :
9 a -b)
2
-100 x -y)
2
= 3 a -b ]
2
- 10 x -y ]
2
= 3 a -b -10 x -y 3 a -b +10 x -y = 3a -3b -10x +10y 3a -3b +10x -10y
Q u e s t i o n : 9 2
Factorize each of the following expression:
(3 + 2a)
2
- 25a
2
S o l u t i o n :
( ( ( [ ( ) [( ) ( )][( ) ( )] ( ) ( )
( ) ( ) ( ) ( )
( ( ( ) ( ) [ ( ]( ) ( ) ( ) ( )
( ( ) ( ) [( ]( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( )
( ( ) ( )
( ) ( ) ( ) ( )
( ( [( ) ][( ) ] ( ) ( )
( ( [ ( ) [ ( ) [ ( ) ( )][ ( ) ( )] ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( ) ( ) ( ) ( ) ( )
Page 3
Q u e s t i o n : 7 4
Factorize each of the following expression:
16x
2
- 25y
2
S o l u t i o n :
16x
2
-25y
2
= 4x)
2
- 5y)
2
= 4x -5y 4x +5y
Q u e s t i o n : 7 5
Factorize each of the following expression:
27x
2
- 12y
2
S o l u t i o n :
27x
2
-12y
2
= 3 9x
2
-4y
2
= 3 3x)
2
- 2y)
2
= 3 3x -2y 3x +2y
Q u e s t i o n : 7 6
Factorize each of the following expression:
144a
2
- 289b
2
S o l u t i o n :
144a
2
-289b
2
= 12a)
2
- 17b)
2
= 12a -17b 12a +17b
Q u e s t i o n : 7 7
Factorize each of the following expression:
12m
2
- 27
S o l u t i o n :
12m
2
-27 = 3 4m
2
-9 = 3 2m)
2
-3
2
= 3 2m -3 2m +3
Q u e s t i o n : 7 8
Factorize each of the following expression:
125x
2
- 45y
2
S o l u t i o n :
125x
2
-45y
2
= 5 25x
2
-9y
2
= 5 5x)
2
- 3y)
2
= 5 5x -3y 5x +3y
Q u e s t i o n : 7 9
Factorize each of the following expression:
144a
2
- 169b
2
S o l u t i o n :
144a
2
-169b
2
= 12a)
2
- 13b)
2
= 12a -13b 12a +13b
Q u e s t i o n : 8 0
Factorize each of the following expression:
(2a - b)
2
- 16c
2
S o l u t i o n :
2a -b)
2
-16c
2
= 2a -b)
2
- 4c)
2
= 2a -b -4c 2a -b +4c = 2a -b -4c 2a -b +4c
Q u e s t i o n : 8 1
Factorize each of the following expression:
(x + 2y)
2
- 4(2x - y)
2
( ( ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ) [( ] ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( )
S o l u t i o n :
x +2y)
2
-4 2x -y)
2
= x +2y)
2
- 2 2x -y ]
2
= x +2y -2 2x -y x +2y +2 2x -y = x +2y -4x +2y x +2y +4x -2y =
Q u e s t i o n : 8 2
Factorize each of the following expression:
3a
5
- 48a
3
S o l u t i o n :
3a
5
-48a
3
= 3a
3
a
2
-16 = 3a
3
a
2
-4
2
= 3a
3
a -4 a +4
Q u e s t i o n : 8 3
Factorize each of the following expression:
a
4
- 16b
4
S o l u t i o n :
a
4
-16b
4
= a
4
-2
4
b
4
= a
2
)
2
- 2
2
b
2
)
2
= a
2
-2
2
b
2
a
2
+2
2
b
2
= a
2
- 2b)
2
a
2
+4b
2
= a -2b a +2b a
2
+4b
2
Q u e s t i o n : 8 4
Factorize each of the following expression:
x
8
- 1
S o l u t i o n :
x
8
-1 = x
4
)
2
-1
2
= x
4
-1 x
4
+1 = x
2
)
2
-1
2
x
4
+1 = x
2
-1 x
2
+1 x
4
+1 = x
2
-1
2
x
2
+1 x
4
+1 = x -1 x +1 x
2
+1 x
4
+1
Q u e s t i o n : 8 5
Factorize each of the following expression:
64 - (a + 1)
2
S o l u t i o n :
64 - a +1)
2
= 8)
2
- a +1)
2
= 8 - a +1 8 + a +1 = 8 -a -1 8 +a +1 = 7 -a 9 +a
Q u e s t i o n : 8 6
Factorize each of the following expression:
36l
2
- (m + n)
2
S o l u t i o n :
36l
2
- m +n)
2
= 6l)
2
- m +n)
2
= 6l - m +n 6l + m +n = 6l -m -n 6l +m +n
Q u e s t i o n : 8 7
Factorize each of the following expression:
25x
4
y
4
- 1
S o l u t i o n :
25x
4
y
4
-1 = 5x
2
y
2
)
2
-1 = 5x
2
y
2
-1 5x
2
y
2
+1
Q u e s t i o n : 8 8
Factorize each of the following expression:
a
4
-
1
b
4
S o l u t i o n :
a
4
- 1/b
4
= (a
2
)
2
- 1/(b
2
)
2
= a
2
- 1/b
2
a
2
+ 1/b
2
= a - 1/ba + 1/ba
2
+ 1/b
2
Q u e s t i o n : 8 9
Factorize each of the following expression:
x
3
- 144x
S o l u t i o n :
x
3
-144x = x x
2
-144 = x x
2
-12
2
= x x -12 x +12
Q u e s t i o n : 9 0
Factorize each of the following expression:
(x - 4y)
2
- 625
S o l u t i o n :
x -4y)
2
-625 = x -4y)
2
-25
2
= x -4y -25 x -4y +25 = x -4y -25 x -4y +25
Q u e s t i o n : 9 1
Factorize each of the following expression:
9(a - b)
2
- 100(x - y)
2
S o l u t i o n :
9 a -b)
2
-100 x -y)
2
= 3 a -b ]
2
- 10 x -y ]
2
= 3 a -b -10 x -y 3 a -b +10 x -y = 3a -3b -10x +10y 3a -3b +10x -10y
Q u e s t i o n : 9 2
Factorize each of the following expression:
(3 + 2a)
2
- 25a
2
S o l u t i o n :
( ( ( [ ( ) [( ) ( )][( ) ( )] ( ) ( )
( ) ( ) ( ) ( )
( ( ( ) ( ) [ ( ]( ) ( ) ( ) ( )
( ( ) ( ) [( ]( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( )
( ( ) ( )
( ) ( ) ( ) ( )
( ( [( ) ][( ) ] ( ) ( )
( ( [ ( ) [ ( ) [ ( ) ( )][ ( ) ( )] ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( ) ( ) ( ) ( ) ( )
3 +2a)
2
-25a
2
= 3 +2a)
2
- 5a)
2
= 3 +2a -5a 3 +2a +5a = 3 +2a -5a 3 +2a +5a = 3 -3a 3 +7a = 3 1 -a 3 +7a
Q u e s t i o n : 9 3
Factorize each of the following expression:
(x + y)
2
- (a - b)
2
S o l u t i o n :
x +y)
2
- a -b)
2
= x +y - a -b x +y + a -b = x +y -a +b x +y +a -b
Q u e s t i o n : 9 4
Factorize each of the following expression:
1
16
x
2
y
2
-
4
49
y
2
z
2
S o l u t i o n :
1
16
x
2
y
2
-
4
49
y
2
z
2
= y
2
1
16
x
2
-
4
49
z
2
= y
2
1
4
x
2
-
2
7
z
2
= y
2
1
4
x -
2
7
z
1
4
x +
2
7
z = y
2
x
4
-
2
7
z
x
4
+
2
7
z
Q u e s t i o n : 9 5
Factorize each of the following expression:
75a
3
b
2
- 108ab
4
S o l u t i o n :
75a
3
b
2
-108ab
4
= 3ab
2
25a
2
-36b
2
= 3ab
2
5a)
2
- 6b)
2
= 3ab
2
5a -6b 5a +6b
Q u e s t i o n : 9 6
Factorize each of the following expression:
x
5
- 16x
3
S o l u t i o n :
x
5
-16x
3
= x
3
x
2
-16 = x
3
x
2
-4
2
= x
3
x -4 x +4
Q u e s t i o n : 9 7
Factorize each of the following expression:
50
x
2
-
2x
2
81
S o l u t i o n :
50
x
2
-
2x
2
81
= 2
25
x
2
-
x
2
81
= 2
5
x
2
-
x
9
2
= 2
5
x
-
x
9
5
x
+
x
9
Q u e s t i o n : 9 8
Factorize each of the following expression:
256x
5
- 81x
S o l u t i o n :
256x
5
-81x = x 256x
4
-81 = x 16x
2
)
2
-9
2
= x 16x
2
+9 16x
2
-9 = x 16x
2
+9 4x)
2
-3
2
= x 16x
2
+9 4x +3 4x -3
Q u e s t i o n : 9 9
Factorize each of the following expression:
a
4
- (2b + c)
4
S o l u t i o n :
a
4
- 2b +c)
4
= a
2
)
2
- 2b +c)
2
]
2
= a
2
+ 2b +c)
2
a
2
- 2b +c)
2
= a
2
+ 2b +c)
2
a + 2b +c a - 2b +c = a
2
+ 2b +c)
2
a +2b +c a -2b -c
Q u e s t i o n : 1 0 0
Factorize each of the following expression:
(3x + 4y)
4
- x
4
S o l u t i o n :
3x +4y)
4
-x
4
= 3x +4y)
2
]
2
- x
2
)
2
= 3x +4y)
2
+x
2
3x +4y)
2
-x
2
= 3x +4y)
2
+x
2
3x +4y +x 3x +4y -x = 3x +4y)
2
+x
2
3x +4y +x 3x +4y -x = (3x +4y)
2
+x
2
4x +4y 2x
Q u e s t i o n : 1 0 1
Factorize each of the following expression:
p
2
q
2
- p
4
q
4
S o l u t i o n :
p2q2-p4q4=p2q2(1-p2q2)=p2q2[1-(pq)2]=p2q2(1-pq)(1+pq)
Q u e s t i o n : 1 0 2
Factorize each of the following expression:
3x
3
y - 243xy
3
S o l u t i o n :
3x3y-243xy3=3xy(x2-81y2)=3xy[x2-(9y)2]=3xy(x-9y)(x+9y)
Q u e s t i o n : 1 0 3
Factorize each of the following expression:
a
4
b
4
- 16c
4
S o l u t i o n :
a4b4-16c4=[(a2b2)2-(4c2)2]=(a2b2+4c2)(a2b2-4c2)=(a2b2+4c2)[(ab)2-(2c)2]=(a2b2+4c2)(ab+2c)(ab-2c)
( ( ( [( ) ][( ) ] ( ) ( ) ( ) ( ) ( ) ( )
( ( [( ) ( )][( ) ( )] ( ) ( )
( ) [ ( ) ( ) ] ( ) ( ) ( ) ( )
( ) [( ( ] ( ) ( )
( ) ( ) ( ) ( )
( ) { ( ) ( ) } ( ) ( )
( ) [( ] ( ) ( ) ( )[( ] ( ) ( ) ( )
( ( [( [ ( ][ ( ] [ ( ]{[ ( )][ ( )]} [ ( ]( ) ( )
( [( ( [( ][( ] [( ][( ) ][( ) ] { ( } ( ) ( ) { } ( ) (
Page 4
Q u e s t i o n : 7 4
Factorize each of the following expression:
16x
2
- 25y
2
S o l u t i o n :
16x
2
-25y
2
= 4x)
2
- 5y)
2
= 4x -5y 4x +5y
Q u e s t i o n : 7 5
Factorize each of the following expression:
27x
2
- 12y
2
S o l u t i o n :
27x
2
-12y
2
= 3 9x
2
-4y
2
= 3 3x)
2
- 2y)
2
= 3 3x -2y 3x +2y
Q u e s t i o n : 7 6
Factorize each of the following expression:
144a
2
- 289b
2
S o l u t i o n :
144a
2
-289b
2
= 12a)
2
- 17b)
2
= 12a -17b 12a +17b
Q u e s t i o n : 7 7
Factorize each of the following expression:
12m
2
- 27
S o l u t i o n :
12m
2
-27 = 3 4m
2
-9 = 3 2m)
2
-3
2
= 3 2m -3 2m +3
Q u e s t i o n : 7 8
Factorize each of the following expression:
125x
2
- 45y
2
S o l u t i o n :
125x
2
-45y
2
= 5 25x
2
-9y
2
= 5 5x)
2
- 3y)
2
= 5 5x -3y 5x +3y
Q u e s t i o n : 7 9
Factorize each of the following expression:
144a
2
- 169b
2
S o l u t i o n :
144a
2
-169b
2
= 12a)
2
- 13b)
2
= 12a -13b 12a +13b
Q u e s t i o n : 8 0
Factorize each of the following expression:
(2a - b)
2
- 16c
2
S o l u t i o n :
2a -b)
2
-16c
2
= 2a -b)
2
- 4c)
2
= 2a -b -4c 2a -b +4c = 2a -b -4c 2a -b +4c
Q u e s t i o n : 8 1
Factorize each of the following expression:
(x + 2y)
2
- 4(2x - y)
2
( ( ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ) [( ] ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( )
S o l u t i o n :
x +2y)
2
-4 2x -y)
2
= x +2y)
2
- 2 2x -y ]
2
= x +2y -2 2x -y x +2y +2 2x -y = x +2y -4x +2y x +2y +4x -2y =
Q u e s t i o n : 8 2
Factorize each of the following expression:
3a
5
- 48a
3
S o l u t i o n :
3a
5
-48a
3
= 3a
3
a
2
-16 = 3a
3
a
2
-4
2
= 3a
3
a -4 a +4
Q u e s t i o n : 8 3
Factorize each of the following expression:
a
4
- 16b
4
S o l u t i o n :
a
4
-16b
4
= a
4
-2
4
b
4
= a
2
)
2
- 2
2
b
2
)
2
= a
2
-2
2
b
2
a
2
+2
2
b
2
= a
2
- 2b)
2
a
2
+4b
2
= a -2b a +2b a
2
+4b
2
Q u e s t i o n : 8 4
Factorize each of the following expression:
x
8
- 1
S o l u t i o n :
x
8
-1 = x
4
)
2
-1
2
= x
4
-1 x
4
+1 = x
2
)
2
-1
2
x
4
+1 = x
2
-1 x
2
+1 x
4
+1 = x
2
-1
2
x
2
+1 x
4
+1 = x -1 x +1 x
2
+1 x
4
+1
Q u e s t i o n : 8 5
Factorize each of the following expression:
64 - (a + 1)
2
S o l u t i o n :
64 - a +1)
2
= 8)
2
- a +1)
2
= 8 - a +1 8 + a +1 = 8 -a -1 8 +a +1 = 7 -a 9 +a
Q u e s t i o n : 8 6
Factorize each of the following expression:
36l
2
- (m + n)
2
S o l u t i o n :
36l
2
- m +n)
2
= 6l)
2
- m +n)
2
= 6l - m +n 6l + m +n = 6l -m -n 6l +m +n
Q u e s t i o n : 8 7
Factorize each of the following expression:
25x
4
y
4
- 1
S o l u t i o n :
25x
4
y
4
-1 = 5x
2
y
2
)
2
-1 = 5x
2
y
2
-1 5x
2
y
2
+1
Q u e s t i o n : 8 8
Factorize each of the following expression:
a
4
-
1
b
4
S o l u t i o n :
a
4
- 1/b
4
= (a
2
)
2
- 1/(b
2
)
2
= a
2
- 1/b
2
a
2
+ 1/b
2
= a - 1/ba + 1/ba
2
+ 1/b
2
Q u e s t i o n : 8 9
Factorize each of the following expression:
x
3
- 144x
S o l u t i o n :
x
3
-144x = x x
2
-144 = x x
2
-12
2
= x x -12 x +12
Q u e s t i o n : 9 0
Factorize each of the following expression:
(x - 4y)
2
- 625
S o l u t i o n :
x -4y)
2
-625 = x -4y)
2
-25
2
= x -4y -25 x -4y +25 = x -4y -25 x -4y +25
Q u e s t i o n : 9 1
Factorize each of the following expression:
9(a - b)
2
- 100(x - y)
2
S o l u t i o n :
9 a -b)
2
-100 x -y)
2
= 3 a -b ]
2
- 10 x -y ]
2
= 3 a -b -10 x -y 3 a -b +10 x -y = 3a -3b -10x +10y 3a -3b +10x -10y
Q u e s t i o n : 9 2
Factorize each of the following expression:
(3 + 2a)
2
- 25a
2
S o l u t i o n :
( ( ( [ ( ) [( ) ( )][( ) ( )] ( ) ( )
( ) ( ) ( ) ( )
( ( ( ) ( ) [ ( ]( ) ( ) ( ) ( )
( ( ) ( ) [( ]( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( )
( ( ) ( )
( ) ( ) ( ) ( )
( ( [( ) ][( ) ] ( ) ( )
( ( [ ( ) [ ( ) [ ( ) ( )][ ( ) ( )] ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( ) ( ) ( ) ( ) ( )
3 +2a)
2
-25a
2
= 3 +2a)
2
- 5a)
2
= 3 +2a -5a 3 +2a +5a = 3 +2a -5a 3 +2a +5a = 3 -3a 3 +7a = 3 1 -a 3 +7a
Q u e s t i o n : 9 3
Factorize each of the following expression:
(x + y)
2
- (a - b)
2
S o l u t i o n :
x +y)
2
- a -b)
2
= x +y - a -b x +y + a -b = x +y -a +b x +y +a -b
Q u e s t i o n : 9 4
Factorize each of the following expression:
1
16
x
2
y
2
-
4
49
y
2
z
2
S o l u t i o n :
1
16
x
2
y
2
-
4
49
y
2
z
2
= y
2
1
16
x
2
-
4
49
z
2
= y
2
1
4
x
2
-
2
7
z
2
= y
2
1
4
x -
2
7
z
1
4
x +
2
7
z = y
2
x
4
-
2
7
z
x
4
+
2
7
z
Q u e s t i o n : 9 5
Factorize each of the following expression:
75a
3
b
2
- 108ab
4
S o l u t i o n :
75a
3
b
2
-108ab
4
= 3ab
2
25a
2
-36b
2
= 3ab
2
5a)
2
- 6b)
2
= 3ab
2
5a -6b 5a +6b
Q u e s t i o n : 9 6
Factorize each of the following expression:
x
5
- 16x
3
S o l u t i o n :
x
5
-16x
3
= x
3
x
2
-16 = x
3
x
2
-4
2
= x
3
x -4 x +4
Q u e s t i o n : 9 7
Factorize each of the following expression:
50
x
2
-
2x
2
81
S o l u t i o n :
50
x
2
-
2x
2
81
= 2
25
x
2
-
x
2
81
= 2
5
x
2
-
x
9
2
= 2
5
x
-
x
9
5
x
+
x
9
Q u e s t i o n : 9 8
Factorize each of the following expression:
256x
5
- 81x
S o l u t i o n :
256x
5
-81x = x 256x
4
-81 = x 16x
2
)
2
-9
2
= x 16x
2
+9 16x
2
-9 = x 16x
2
+9 4x)
2
-3
2
= x 16x
2
+9 4x +3 4x -3
Q u e s t i o n : 9 9
Factorize each of the following expression:
a
4
- (2b + c)
4
S o l u t i o n :
a
4
- 2b +c)
4
= a
2
)
2
- 2b +c)
2
]
2
= a
2
+ 2b +c)
2
a
2
- 2b +c)
2
= a
2
+ 2b +c)
2
a + 2b +c a - 2b +c = a
2
+ 2b +c)
2
a +2b +c a -2b -c
Q u e s t i o n : 1 0 0
Factorize each of the following expression:
(3x + 4y)
4
- x
4
S o l u t i o n :
3x +4y)
4
-x
4
= 3x +4y)
2
]
2
- x
2
)
2
= 3x +4y)
2
+x
2
3x +4y)
2
-x
2
= 3x +4y)
2
+x
2
3x +4y +x 3x +4y -x = 3x +4y)
2
+x
2
3x +4y +x 3x +4y -x = (3x +4y)
2
+x
2
4x +4y 2x
Q u e s t i o n : 1 0 1
Factorize each of the following expression:
p
2
q
2
- p
4
q
4
S o l u t i o n :
p2q2-p4q4=p2q2(1-p2q2)=p2q2[1-(pq)2]=p2q2(1-pq)(1+pq)
Q u e s t i o n : 1 0 2
Factorize each of the following expression:
3x
3
y - 243xy
3
S o l u t i o n :
3x3y-243xy3=3xy(x2-81y2)=3xy[x2-(9y)2]=3xy(x-9y)(x+9y)
Q u e s t i o n : 1 0 3
Factorize each of the following expression:
a
4
b
4
- 16c
4
S o l u t i o n :
a4b4-16c4=[(a2b2)2-(4c2)2]=(a2b2+4c2)(a2b2-4c2)=(a2b2+4c2)[(ab)2-(2c)2]=(a2b2+4c2)(ab+2c)(ab-2c)
( ( ( [( ) ][( ) ] ( ) ( ) ( ) ( ) ( ) ( )
( ( [( ) ( )][( ) ( )] ( ) ( )
( ) [ ( ) ( ) ] ( ) ( ) ( ) ( )
( ) [( ( ] ( ) ( )
( ) ( ) ( ) ( )
( ) { ( ) ( ) } ( ) ( )
( ) [( ] ( ) ( ) ( )[( ] ( ) ( ) ( )
( ( [( [ ( ][ ( ] [ ( ]{[ ( )][ ( )]} [ ( ]( ) ( )
( [( ( [( ][( ] [( ][( ) ][( ) ] { ( } ( ) ( ) { } ( ) (
Q u e s t i o n : 1 0 4
Factorize each of the following expression:
x
4
- 625
S o l u t i o n :
x4-625=(x2)2-252=(x2+25)(x2-25)=(x2+25)(x2-52)=(x2+25)(x+5)(x-5)
Q u e s t i o n : 1 0 5
Factorize each of the following expression:
x
4
- 1
S o l u t i o n :
x4-1=(x2)2-1=(x2+1)(x2-1)=(x2+1)(x+1)(x-1)
Q u e s t i o n : 1 0 6
Factorize each of the following expression:
49(a - b)
2
- 25(a + b)
2
S o l u t i o n :
49(a-b)2-25(a+b)2=[7(a-b)]2-[5(a+b)]2=[7(a-b)-5(a+b)][7(a-b)+5(a+b)]=(7a-7b-5a-5b)(7a-7b+5a+5b)=(2a-12b)(12a-2b)=2(a-6b)2(6a-b)=4(a-6b)(6a-b)
Q u e s t i o n : 1 0 7
Factorize each of the following expression:
x - y - x
2
+ y
2
S o l u t i o n :
x-y-x2+y2=(x-y)+(y2-x2) [Regrouping the terms]=(x-y)+(y+x)(y-x)=(x-y)-(y+x)(x-y) [ ?(y-x)=-(x-y)]=(x-y)[1-(y+x)]=(x-y)(1-x-y)
Q u e s t i o n : 1 0 8
Factorize each of the following expression:
16(2x - 1)
2
- 25y
2
S o l u t i o n :
16(2x-1)2-25y2=[4(2x-1)]2-(5y)2=[4(2x-1)-5y][4(2x-1)+5y]=(8x-4-5y)(8x-4+5y)=(8x-5y-4)(8x+5y-4)
Q u e s t i o n : 1 0 9
Factorize each of the following expression:
4(xy + 1)
2
- 9(x - 1)
2
S o l u t i o n :
4(xy+1)2-9(x-1)2=[2(xy+1)]2-[3(x-1)]2=[2(xy+1)-3(x-1)][2(xy+1)+3(x-1)]=(2xy+2-3x+3)(2xy+2+3x-3)=(2xy-3x+5)(2xy+3x-1)
Q u e s t i o n : 1 1 0
Factorize each of the following expression:
(2x + 1)
2
- 9x
4
S o l u t i o n :
(2x+1)2-9x4=(2x+1)2-(3x2)2=[(2x+1)-3x2][(2x+1)+3x2]=(-3x2+2x+1)(3x2+2x+1)We can factorise the quadratic expressions in the curved brackets as:(-3x2+3x-x+1)(3x2+2x+1)=3x(-x+1)+1(-x
=(-x+1)(3x+1)(3x2+2x+1)=-(x-1)(3x+1)(3x2+2x+1)
Q u e s t i o n : 1 1 1
Factorize each of the following expression:
x
4
- (2y - 3z)
2
S o l u t i o n :
x4-(2y-3z)2=(x2)2-(2y-3z)2=[x2-(2y-3z)][x2+(2y-3z)]=(x2-2y+3z)(x2+2y-3z)
Q u e s t i o n : 1 1 2
Factorize each of the following expression:
a
2
- b
2
+ a - b
S o l u t i o n :
a2-b2+a-b=(a2-b2)+(a-b) [Grouping the terms] =(a+b)(a-b)+(a-b) =(a-b)(a+b+1) [Taking out the common factor (a-b)]
Q u e s t i o n : 1 1 3
Factorize each of the following expression:
16a
4
- b
4
S o l u t i o n :
16a4-b4=(4a2)2-(b2)2=(4a2+b2)(4a2-b2)=(4a2+b2)[(2a)2-b2]=(4a2+b2)(2a+b)(2a-b)
Q u e s t i o n : 1 1 4
Factorize each of the following expression:
a
4
- 16(b - c)
4
S o l u t i o n :
a4-16(b-c)4=(a2)2-[4(b-c)2]2=[a2+4(b-c)2][a2-4(b-c)2]=[a2+4(b-c)2]{a2-[2(b-c)]2}=[a2+4(b-c)2][a+2(b-c)][a-2(b-c)]=[a2+4(b-c)2](a+2b-2c)(a-2b+2c)
Q u e s t i o n : 1 1 5
Factorize each of the following expression:
2a
5
- 32a
S o l u t i o n :
2a5-32a=2a(a4-16)=2a[(a2)2-42]=2a(a2+4)(a2-4)=2a(a2+4)(a2-22)=2a(a2+4)(a+2)(a-2)=2a(a-2)(a+2)(a2+4)
Q u e s t i o n : 1 1 6
Factorize each of the following expression:
a
4
b
4
- 81c
4
S o l u t i o n :
a4b4-81c4=(a2b2)2-(9c2)2=(a2b2+9c2)(a2b2-9c2)=(a2b2+9c2)[(ab)2-(3c)2]=(a2b2+9c2)(ab+3c)(ab-3c)
Page 5
Q u e s t i o n : 7 4
Factorize each of the following expression:
16x
2
- 25y
2
S o l u t i o n :
16x
2
-25y
2
= 4x)
2
- 5y)
2
= 4x -5y 4x +5y
Q u e s t i o n : 7 5
Factorize each of the following expression:
27x
2
- 12y
2
S o l u t i o n :
27x
2
-12y
2
= 3 9x
2
-4y
2
= 3 3x)
2
- 2y)
2
= 3 3x -2y 3x +2y
Q u e s t i o n : 7 6
Factorize each of the following expression:
144a
2
- 289b
2
S o l u t i o n :
144a
2
-289b
2
= 12a)
2
- 17b)
2
= 12a -17b 12a +17b
Q u e s t i o n : 7 7
Factorize each of the following expression:
12m
2
- 27
S o l u t i o n :
12m
2
-27 = 3 4m
2
-9 = 3 2m)
2
-3
2
= 3 2m -3 2m +3
Q u e s t i o n : 7 8
Factorize each of the following expression:
125x
2
- 45y
2
S o l u t i o n :
125x
2
-45y
2
= 5 25x
2
-9y
2
= 5 5x)
2
- 3y)
2
= 5 5x -3y 5x +3y
Q u e s t i o n : 7 9
Factorize each of the following expression:
144a
2
- 169b
2
S o l u t i o n :
144a
2
-169b
2
= 12a)
2
- 13b)
2
= 12a -13b 12a +13b
Q u e s t i o n : 8 0
Factorize each of the following expression:
(2a - b)
2
- 16c
2
S o l u t i o n :
2a -b)
2
-16c
2
= 2a -b)
2
- 4c)
2
= 2a -b -4c 2a -b +4c = 2a -b -4c 2a -b +4c
Q u e s t i o n : 8 1
Factorize each of the following expression:
(x + 2y)
2
- 4(2x - y)
2
( ( ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ) [( ] ( ) ( )
( ) [( ( ] ( ) ( )
( ( ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( )
S o l u t i o n :
x +2y)
2
-4 2x -y)
2
= x +2y)
2
- 2 2x -y ]
2
= x +2y -2 2x -y x +2y +2 2x -y = x +2y -4x +2y x +2y +4x -2y =
Q u e s t i o n : 8 2
Factorize each of the following expression:
3a
5
- 48a
3
S o l u t i o n :
3a
5
-48a
3
= 3a
3
a
2
-16 = 3a
3
a
2
-4
2
= 3a
3
a -4 a +4
Q u e s t i o n : 8 3
Factorize each of the following expression:
a
4
- 16b
4
S o l u t i o n :
a
4
-16b
4
= a
4
-2
4
b
4
= a
2
)
2
- 2
2
b
2
)
2
= a
2
-2
2
b
2
a
2
+2
2
b
2
= a
2
- 2b)
2
a
2
+4b
2
= a -2b a +2b a
2
+4b
2
Q u e s t i o n : 8 4
Factorize each of the following expression:
x
8
- 1
S o l u t i o n :
x
8
-1 = x
4
)
2
-1
2
= x
4
-1 x
4
+1 = x
2
)
2
-1
2
x
4
+1 = x
2
-1 x
2
+1 x
4
+1 = x
2
-1
2
x
2
+1 x
4
+1 = x -1 x +1 x
2
+1 x
4
+1
Q u e s t i o n : 8 5
Factorize each of the following expression:
64 - (a + 1)
2
S o l u t i o n :
64 - a +1)
2
= 8)
2
- a +1)
2
= 8 - a +1 8 + a +1 = 8 -a -1 8 +a +1 = 7 -a 9 +a
Q u e s t i o n : 8 6
Factorize each of the following expression:
36l
2
- (m + n)
2
S o l u t i o n :
36l
2
- m +n)
2
= 6l)
2
- m +n)
2
= 6l - m +n 6l + m +n = 6l -m -n 6l +m +n
Q u e s t i o n : 8 7
Factorize each of the following expression:
25x
4
y
4
- 1
S o l u t i o n :
25x
4
y
4
-1 = 5x
2
y
2
)
2
-1 = 5x
2
y
2
-1 5x
2
y
2
+1
Q u e s t i o n : 8 8
Factorize each of the following expression:
a
4
-
1
b
4
S o l u t i o n :
a
4
- 1/b
4
= (a
2
)
2
- 1/(b
2
)
2
= a
2
- 1/b
2
a
2
+ 1/b
2
= a - 1/ba + 1/ba
2
+ 1/b
2
Q u e s t i o n : 8 9
Factorize each of the following expression:
x
3
- 144x
S o l u t i o n :
x
3
-144x = x x
2
-144 = x x
2
-12
2
= x x -12 x +12
Q u e s t i o n : 9 0
Factorize each of the following expression:
(x - 4y)
2
- 625
S o l u t i o n :
x -4y)
2
-625 = x -4y)
2
-25
2
= x -4y -25 x -4y +25 = x -4y -25 x -4y +25
Q u e s t i o n : 9 1
Factorize each of the following expression:
9(a - b)
2
- 100(x - y)
2
S o l u t i o n :
9 a -b)
2
-100 x -y)
2
= 3 a -b ]
2
- 10 x -y ]
2
= 3 a -b -10 x -y 3 a -b +10 x -y = 3a -3b -10x +10y 3a -3b +10x -10y
Q u e s t i o n : 9 2
Factorize each of the following expression:
(3 + 2a)
2
- 25a
2
S o l u t i o n :
( ( ( [ ( ) [( ) ( )][( ) ( )] ( ) ( )
( ) ( ) ( ) ( )
( ( ( ) ( ) [ ( ]( ) ( ) ( ) ( )
( ( ) ( ) [( ]( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( ) ( ) ( )
( ( ( [ ( )][ ( )] ( ) ( )
( ( ) ( )
( ) ( ) ( ) ( )
( ( [( ) ][( ) ] ( ) ( )
( ( [ ( ) [ ( ) [ ( ) ( )][ ( ) ( )] ( ) ( )
( ( ( [( ) ][( ) ] ( ) ( ) ( ) ( ) ( ) ( )
3 +2a)
2
-25a
2
= 3 +2a)
2
- 5a)
2
= 3 +2a -5a 3 +2a +5a = 3 +2a -5a 3 +2a +5a = 3 -3a 3 +7a = 3 1 -a 3 +7a
Q u e s t i o n : 9 3
Factorize each of the following expression:
(x + y)
2
- (a - b)
2
S o l u t i o n :
x +y)
2
- a -b)
2
= x +y - a -b x +y + a -b = x +y -a +b x +y +a -b
Q u e s t i o n : 9 4
Factorize each of the following expression:
1
16
x
2
y
2
-
4
49
y
2
z
2
S o l u t i o n :
1
16
x
2
y
2
-
4
49
y
2
z
2
= y
2
1
16
x
2
-
4
49
z
2
= y
2
1
4
x
2
-
2
7
z
2
= y
2
1
4
x -
2
7
z
1
4
x +
2
7
z = y
2
x
4
-
2
7
z
x
4
+
2
7
z
Q u e s t i o n : 9 5
Factorize each of the following expression:
75a
3
b
2
- 108ab
4
S o l u t i o n :
75a
3
b
2
-108ab
4
= 3ab
2
25a
2
-36b
2
= 3ab
2
5a)
2
- 6b)
2
= 3ab
2
5a -6b 5a +6b
Q u e s t i o n : 9 6
Factorize each of the following expression:
x
5
- 16x
3
S o l u t i o n :
x
5
-16x
3
= x
3
x
2
-16 = x
3
x
2
-4
2
= x
3
x -4 x +4
Q u e s t i o n : 9 7
Factorize each of the following expression:
50
x
2
-
2x
2
81
S o l u t i o n :
50
x
2
-
2x
2
81
= 2
25
x
2
-
x
2
81
= 2
5
x
2
-
x
9
2
= 2
5
x
-
x
9
5
x
+
x
9
Q u e s t i o n : 9 8
Factorize each of the following expression:
256x
5
- 81x
S o l u t i o n :
256x
5
-81x = x 256x
4
-81 = x 16x
2
)
2
-9
2
= x 16x
2
+9 16x
2
-9 = x 16x
2
+9 4x)
2
-3
2
= x 16x
2
+9 4x +3 4x -3
Q u e s t i o n : 9 9
Factorize each of the following expression:
a
4
- (2b + c)
4
S o l u t i o n :
a
4
- 2b +c)
4
= a
2
)
2
- 2b +c)
2
]
2
= a
2
+ 2b +c)
2
a
2
- 2b +c)
2
= a
2
+ 2b +c)
2
a + 2b +c a - 2b +c = a
2
+ 2b +c)
2
a +2b +c a -2b -c
Q u e s t i o n : 1 0 0
Factorize each of the following expression:
(3x + 4y)
4
- x
4
S o l u t i o n :
3x +4y)
4
-x
4
= 3x +4y)
2
]
2
- x
2
)
2
= 3x +4y)
2
+x
2
3x +4y)
2
-x
2
= 3x +4y)
2
+x
2
3x +4y +x 3x +4y -x = 3x +4y)
2
+x
2
3x +4y +x 3x +4y -x = (3x +4y)
2
+x
2
4x +4y 2x
Q u e s t i o n : 1 0 1
Factorize each of the following expression:
p
2
q
2
- p
4
q
4
S o l u t i o n :
p2q2-p4q4=p2q2(1-p2q2)=p2q2[1-(pq)2]=p2q2(1-pq)(1+pq)
Q u e s t i o n : 1 0 2
Factorize each of the following expression:
3x
3
y - 243xy
3
S o l u t i o n :
3x3y-243xy3=3xy(x2-81y2)=3xy[x2-(9y)2]=3xy(x-9y)(x+9y)
Q u e s t i o n : 1 0 3
Factorize each of the following expression:
a
4
b
4
- 16c
4
S o l u t i o n :
a4b4-16c4=[(a2b2)2-(4c2)2]=(a2b2+4c2)(a2b2-4c2)=(a2b2+4c2)[(ab)2-(2c)2]=(a2b2+4c2)(ab+2c)(ab-2c)
( ( ( [( ) ][( ) ] ( ) ( ) ( ) ( ) ( ) ( )
( ( [( ) ( )][( ) ( )] ( ) ( )
( ) [ ( ) ( ) ] ( ) ( ) ( ) ( )
( ) [( ( ] ( ) ( )
( ) ( ) ( ) ( )
( ) { ( ) ( ) } ( ) ( )
( ) [( ] ( ) ( ) ( )[( ] ( ) ( ) ( )
( ( [( [ ( ][ ( ] [ ( ]{[ ( )][ ( )]} [ ( ]( ) ( )
( [( ( [( ][( ] [( ][( ) ][( ) ] { ( } ( ) ( ) { } ( ) (
Q u e s t i o n : 1 0 4
Factorize each of the following expression:
x
4
- 625
S o l u t i o n :
x4-625=(x2)2-252=(x2+25)(x2-25)=(x2+25)(x2-52)=(x2+25)(x+5)(x-5)
Q u e s t i o n : 1 0 5
Factorize each of the following expression:
x
4
- 1
S o l u t i o n :
x4-1=(x2)2-1=(x2+1)(x2-1)=(x2+1)(x+1)(x-1)
Q u e s t i o n : 1 0 6
Factorize each of the following expression:
49(a - b)
2
- 25(a + b)
2
S o l u t i o n :
49(a-b)2-25(a+b)2=[7(a-b)]2-[5(a+b)]2=[7(a-b)-5(a+b)][7(a-b)+5(a+b)]=(7a-7b-5a-5b)(7a-7b+5a+5b)=(2a-12b)(12a-2b)=2(a-6b)2(6a-b)=4(a-6b)(6a-b)
Q u e s t i o n : 1 0 7
Factorize each of the following expression:
x - y - x
2
+ y
2
S o l u t i o n :
x-y-x2+y2=(x-y)+(y2-x2) [Regrouping the terms]=(x-y)+(y+x)(y-x)=(x-y)-(y+x)(x-y) [ ?(y-x)=-(x-y)]=(x-y)[1-(y+x)]=(x-y)(1-x-y)
Q u e s t i o n : 1 0 8
Factorize each of the following expression:
16(2x - 1)
2
- 25y
2
S o l u t i o n :
16(2x-1)2-25y2=[4(2x-1)]2-(5y)2=[4(2x-1)-5y][4(2x-1)+5y]=(8x-4-5y)(8x-4+5y)=(8x-5y-4)(8x+5y-4)
Q u e s t i o n : 1 0 9
Factorize each of the following expression:
4(xy + 1)
2
- 9(x - 1)
2
S o l u t i o n :
4(xy+1)2-9(x-1)2=[2(xy+1)]2-[3(x-1)]2=[2(xy+1)-3(x-1)][2(xy+1)+3(x-1)]=(2xy+2-3x+3)(2xy+2+3x-3)=(2xy-3x+5)(2xy+3x-1)
Q u e s t i o n : 1 1 0
Factorize each of the following expression:
(2x + 1)
2
- 9x
4
S o l u t i o n :
(2x+1)2-9x4=(2x+1)2-(3x2)2=[(2x+1)-3x2][(2x+1)+3x2]=(-3x2+2x+1)(3x2+2x+1)We can factorise the quadratic expressions in the curved brackets as:(-3x2+3x-x+1)(3x2+2x+1)=3x(-x+1)+1(-x
=(-x+1)(3x+1)(3x2+2x+1)=-(x-1)(3x+1)(3x2+2x+1)
Q u e s t i o n : 1 1 1
Factorize each of the following expression:
x
4
- (2y - 3z)
2
S o l u t i o n :
x4-(2y-3z)2=(x2)2-(2y-3z)2=[x2-(2y-3z)][x2+(2y-3z)]=(x2-2y+3z)(x2+2y-3z)
Q u e s t i o n : 1 1 2
Factorize each of the following expression:
a
2
- b
2
+ a - b
S o l u t i o n :
a2-b2+a-b=(a2-b2)+(a-b) [Grouping the terms] =(a+b)(a-b)+(a-b) =(a-b)(a+b+1) [Taking out the common factor (a-b)]
Q u e s t i o n : 1 1 3
Factorize each of the following expression:
16a
4
- b
4
S o l u t i o n :
16a4-b4=(4a2)2-(b2)2=(4a2+b2)(4a2-b2)=(4a2+b2)[(2a)2-b2]=(4a2+b2)(2a+b)(2a-b)
Q u e s t i o n : 1 1 4
Factorize each of the following expression:
a
4
- 16(b - c)
4
S o l u t i o n :
a4-16(b-c)4=(a2)2-[4(b-c)2]2=[a2+4(b-c)2][a2-4(b-c)2]=[a2+4(b-c)2]{a2-[2(b-c)]2}=[a2+4(b-c)2][a+2(b-c)][a-2(b-c)]=[a2+4(b-c)2](a+2b-2c)(a-2b+2c)
Q u e s t i o n : 1 1 5
Factorize each of the following expression:
2a
5
- 32a
S o l u t i o n :
2a5-32a=2a(a4-16)=2a[(a2)2-42]=2a(a2+4)(a2-4)=2a(a2+4)(a2-22)=2a(a2+4)(a+2)(a-2)=2a(a-2)(a+2)(a2+4)
Q u e s t i o n : 1 1 6
Factorize each of the following expression:
a
4
b
4
- 81c
4
S o l u t i o n :
a4b4-81c4=(a2b2)2-(9c2)2=(a2b2+9c2)(a2b2-9c2)=(a2b2+9c2)[(ab)2-(3c)2]=(a2b2+9c2)(ab+3c)(ab-3c)
Q u e s t i o n : 1 1 7
Factorize each of the following expression:
xy
9
- yx
9
S o l u t i o n :
xy9-yx9=xy(y8-x8)=xy[(y4)2-(x4)2]=xy(y4+x4)(y4-x4)=xy(y4+x4)[(y2)2-(x2)2]=xy(y4+x4)(y2+x2)(y2-x2)=xy(y4+x4)(y2+x2)(y+x)(y-x)
Q u e s t i o n : 1 1 8
Factorize each of the following expression:
x
3
- x
S o l u t i o n :
x3-x=x(x2-1)=x(x-1)(x+1)
Q u e s t i o n : 1 1 9
Factorize each of the following expression:
18a
2
x
2
- 32
S o l u t i o n :
18a2x2-32=2(9a2x2-16)=2[(3ax)2-42]=2(3ax-4)(3ax+4)
Read More
|
79 videos|408 docs|31 tests
|
Related Exams
About this Document
|
4.75/5 Rating |
|
Dec 04, 2024 Last updated |
Document Description: Factorization - Exercise 7.5 for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
The notes and questions for Factorization - Exercise 7.5 have been prepared according to the Class 8 exam syllabus. Information about Factorization - Exercise 7.5 covers topics
like and Factorization - Exercise 7.5 Example, for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Factorization - Exercise 7.5.
Introduction of Factorization - Exercise 7.5 in English is available as part of our Mathematics (Maths) Class 8
for Class 8 & Factorization - Exercise 7.5 in Hindi for Mathematics (Maths) Class 8 course.
Download more important topics related with notes, lectures and mock test series for Class 8
Exam by signing up for free. Class 8: Factorization - Exercise 7.5 | Mathematics (Maths) Class 8
Description
Full syllabus notes, lecture & questions for Factorization - Exercise 7.5 | Mathematics (Maths) Class 8 - Class 8 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 8 | Best notes, free PDF download
Information about Factorization - Exercise 7.5
In this doc you can find the meaning of Factorization - Exercise 7.5 defined & explained in the simplest way possible. Besides explaining types of
Factorization - Exercise 7.5 theory, EduRev gives you an ample number of questions to practice Factorization - Exercise 7.5 tests, examples and also practice Class 8
tests
|
Explore Courses for Class 8 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Exam
,video lectures
,MCQs
,Factorization - Exercise 7.5 | Mathematics (Maths) Class 8
,study material
,Extra Questions
,Factorization - Exercise 7.5 | Mathematics (Maths) Class 8
,shortcuts and tricks
,mock tests for examination
,Important questions
,Sample Paper
,ppt
,Factorization - Exercise 7.5 | Mathematics (Maths) Class 8
,Previous Year Questions with Solutions
,Objective type Questions
,Free
,Viva Questions
,Semester Notes
,past year papers
,Summary
,practice quizzes
;
Additional Information about Factorization - Exercise 7.5 for Class 8 Preparation
Factorization - Exercise 7.5 Free PDF Download
The Factorization - Exercise 7.5 is an invaluable resource that delves deep into the core of the Class 8 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Factorization - Exercise 7.5 now and kickstart your journey towards success in the Class 8 exam.
Importance of Factorization - Exercise 7.5
The importance of Factorization - Exercise 7.5 cannot be overstated, especially for Class 8 aspirants.
This document holds the key to success in the Class 8 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Factorization - Exercise 7.5 Notes
Factorization - Exercise 7.5 Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Factorization - Exercise 7.5.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Factorization - Exercise 7.5 Notes on EduRev are your ultimate resource for success.
Factorization - Exercise 7.5 Class 8 Questions
The "Factorization - Exercise 7.5 Class 8 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 8 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Factorization - Exercise 7.5 on the App
Students of Class 8 can study Factorization - Exercise 7.5 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Factorization - Exercise 7.5,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Factorization - Exercise 7.5 is prepared as per the latest Class 8 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup