Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Factorization - Exercise 7.5
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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)
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