Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 7C - Factorisation
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Page 2
Factorise:
x
2
+ 14x + 49
S o l u t i o n :
We have:
x
2
+14x +49 = x
2
+2 ×x ×7 +(7)
2
= (x +7)
2
? x
2
+14x +49 = (x +7)
2
Q u e s t i o n : 5 9
Factorise:
1 + 2x + x
2
S o l u t i o n :
We have:
1 +2x +x
2
= x
2
+2x +1 = x
2
+2 ×x ×1 +(1)
2
= (x +1)
2
? 1 +2x +x
2
= (x +1)
2
Q u e s t i o n : 6 0
Factorise:
9 + 6z + z
2
S o l u t i o n :
We have;
9 +6z +z
2
= z
2
+6z +9 = z
2
+2 ×x ×3 +(3)
2
= (z +3)
2
? 9 +6z +z
2
= (z +3)
2
Q u e s t i o n : 6 1
Factorise:
x
2
+ 6ax + 9a
2
S o l u t i o n :
We have:
x
2
+6ax +9a
2
= x
2
+2 ×x ×3a +(3a)
2
= (x +3a)
2
? x
2
+6ax +9a
2
= (x +3a)
2
Q u e s t i o n : 6 2
Factorise:
4y
2
+ 20y + 25
S o l u t i o n :
We have:
4y
2
+20y +25 = (2y)
2
+2 ×2y ×5 +(5)
2
= (2y +5)
2
? 4y
2
+20y +25 = (2y +5)
2
Q u e s t i o n : 6 3
Factorise:
36a
2
+ 36a + 9
S o l u t i o n :
We have:
36a
2
+36a +9 = (6a)
2
+2 ×6a ×3 +(3)
2
= (6a +3)
2
? 36a
2
+36a +9 = (6a +3)
2
Q u e s t i o n : 6 4
Factorise:
9m
2
+ 24m + 16
S o l u t i o n :
We have:
9m
2
+24m +16 = (3m)
2
+2 ×3m ×4 +(4)
2
= (3m +4)
2
? 9m
2
+24m +16 = (3m +4)
2
Q u e s t i o n : 6 5
Factorise:
z
2
+ z +
1
4
S o l u t i o n :
We have:
z
2
+z +
1
4
= z
2
+2 ×z ×
1
2
×
1
2
2
= z +
1
2
2
? z
2
+z +
1
4
= z +
1
2
2
Q u e s t i o n : 6 6
Factorise:
49a
2
+ 84ab + 36b
2
S o l u t i o n :
We have:
( )
( )
( )
Page 3
Factorise:
x
2
+ 14x + 49
S o l u t i o n :
We have:
x
2
+14x +49 = x
2
+2 ×x ×7 +(7)
2
= (x +7)
2
? x
2
+14x +49 = (x +7)
2
Q u e s t i o n : 5 9
Factorise:
1 + 2x + x
2
S o l u t i o n :
We have:
1 +2x +x
2
= x
2
+2x +1 = x
2
+2 ×x ×1 +(1)
2
= (x +1)
2
? 1 +2x +x
2
= (x +1)
2
Q u e s t i o n : 6 0
Factorise:
9 + 6z + z
2
S o l u t i o n :
We have;
9 +6z +z
2
= z
2
+6z +9 = z
2
+2 ×x ×3 +(3)
2
= (z +3)
2
? 9 +6z +z
2
= (z +3)
2
Q u e s t i o n : 6 1
Factorise:
x
2
+ 6ax + 9a
2
S o l u t i o n :
We have:
x
2
+6ax +9a
2
= x
2
+2 ×x ×3a +(3a)
2
= (x +3a)
2
? x
2
+6ax +9a
2
= (x +3a)
2
Q u e s t i o n : 6 2
Factorise:
4y
2
+ 20y + 25
S o l u t i o n :
We have:
4y
2
+20y +25 = (2y)
2
+2 ×2y ×5 +(5)
2
= (2y +5)
2
? 4y
2
+20y +25 = (2y +5)
2
Q u e s t i o n : 6 3
Factorise:
36a
2
+ 36a + 9
S o l u t i o n :
We have:
36a
2
+36a +9 = (6a)
2
+2 ×6a ×3 +(3)
2
= (6a +3)
2
? 36a
2
+36a +9 = (6a +3)
2
Q u e s t i o n : 6 4
Factorise:
9m
2
+ 24m + 16
S o l u t i o n :
We have:
9m
2
+24m +16 = (3m)
2
+2 ×3m ×4 +(4)
2
= (3m +4)
2
? 9m
2
+24m +16 = (3m +4)
2
Q u e s t i o n : 6 5
Factorise:
z
2
+ z +
1
4
S o l u t i o n :
We have:
z
2
+z +
1
4
= z
2
+2 ×z ×
1
2
×
1
2
2
= z +
1
2
2
? z
2
+z +
1
4
= z +
1
2
2
Q u e s t i o n : 6 6
Factorise:
49a
2
+ 84ab + 36b
2
S o l u t i o n :
We have:
( )
( )
( )
49a
2
+84ab +36b
2
= (7a)
2
+2 ×7a ×6b +(6b)
2
= (7a +6b)
2
? 49a
2
+84ab +36b
2
= (7a +6b)
2
Q u e s t i o n : 6 7
Factorise:
p
2
- 10p + 25
S o l u t i o n :
We have:
p
2
-10p +25 = p
2
-2 ×p ×5 +(5)
2
= (p -5)
2
? p
2
-10p +25 = (p -5)
2
Q u e s t i o n : 6 8
Factorise:
121a
2
- 88ab + 16b
2
S o l u t i o n :
We have:
121a
2
-88ab +16b
2
= (11a)
2
-2 ×11a ×4b +(4b)
2
= (11a -4b)
2
? 121a
2
-88ab +16b
2
= (11a -4b)
2
Q u e s t i o n : 6 9
Factorise:
1 - 6x + 9x
2
S o l u t i o n :
We have:
1 -6x +9x
2
= 9x
2
-6x +1
= (3x)
2
-2 ×3x ×1 +(1)
2
= (3x -1)
2
? 1 -6x +9x
2
= (3x -1)
2
Q u e s t i o n : 7 0
Factorise:
9y
2
- 12y + 4
S o l u t i o n :
We have:
9y
2
-12y +4 = (3y)
2
-2 ×3y ×2 +(2)
2
= (3y -2)
2
? 9y
2
-12y +4 = (3y -2)
2
Q u e s t i o n : 7 1
Factorise:
16x
2
- 24x + 9
S o l u t i o n :
We have:
16x
2
-24x +9 = (4x)
2
-2 ×4x ×3 +(3)
2
= (4x -3)
2
? 16x
2
-24x +9 = (4x -3)
2
Q u e s t i o n : 7 2
Factorise:
m
2
- 4mn + 4n
2
S o l u t i o n :
We have:
m
2
-4mn +4n
2
= m
2
-2 ×m ×2n +(2n)
2
= (m -2n)
2
? m
2
-4mn +4n
2
= (m -2n)
2
Q u e s t i o n : 7 3
Factorise:
a
2
b
2
- 6abc + 9c
2
S o l u t i o n :
We have:
a
2
b
2
-6abc +9c
2
= (ab)
2
-2 ×ab ×3c +(3c)
2
= (ab -3c)
2
Q u e s t i o n : 7 4
Factorise:
m
4
+ 2m
2
n
2
+ n
4
S o l u t i o n :
We have:
m
4
+2m
2
n
2
+n
4
= m
2
2
+2 ×m
2
×n
2
+ n
2
2
= m
2
+n
2
2
? m
4
+2m
2
n
2
+n
4
= m
2
+n
2
2
( ) ( )
( )
( )
Page 4
Factorise:
x
2
+ 14x + 49
S o l u t i o n :
We have:
x
2
+14x +49 = x
2
+2 ×x ×7 +(7)
2
= (x +7)
2
? x
2
+14x +49 = (x +7)
2
Q u e s t i o n : 5 9
Factorise:
1 + 2x + x
2
S o l u t i o n :
We have:
1 +2x +x
2
= x
2
+2x +1 = x
2
+2 ×x ×1 +(1)
2
= (x +1)
2
? 1 +2x +x
2
= (x +1)
2
Q u e s t i o n : 6 0
Factorise:
9 + 6z + z
2
S o l u t i o n :
We have;
9 +6z +z
2
= z
2
+6z +9 = z
2
+2 ×x ×3 +(3)
2
= (z +3)
2
? 9 +6z +z
2
= (z +3)
2
Q u e s t i o n : 6 1
Factorise:
x
2
+ 6ax + 9a
2
S o l u t i o n :
We have:
x
2
+6ax +9a
2
= x
2
+2 ×x ×3a +(3a)
2
= (x +3a)
2
? x
2
+6ax +9a
2
= (x +3a)
2
Q u e s t i o n : 6 2
Factorise:
4y
2
+ 20y + 25
S o l u t i o n :
We have:
4y
2
+20y +25 = (2y)
2
+2 ×2y ×5 +(5)
2
= (2y +5)
2
? 4y
2
+20y +25 = (2y +5)
2
Q u e s t i o n : 6 3
Factorise:
36a
2
+ 36a + 9
S o l u t i o n :
We have:
36a
2
+36a +9 = (6a)
2
+2 ×6a ×3 +(3)
2
= (6a +3)
2
? 36a
2
+36a +9 = (6a +3)
2
Q u e s t i o n : 6 4
Factorise:
9m
2
+ 24m + 16
S o l u t i o n :
We have:
9m
2
+24m +16 = (3m)
2
+2 ×3m ×4 +(4)
2
= (3m +4)
2
? 9m
2
+24m +16 = (3m +4)
2
Q u e s t i o n : 6 5
Factorise:
z
2
+ z +
1
4
S o l u t i o n :
We have:
z
2
+z +
1
4
= z
2
+2 ×z ×
1
2
×
1
2
2
= z +
1
2
2
? z
2
+z +
1
4
= z +
1
2
2
Q u e s t i o n : 6 6
Factorise:
49a
2
+ 84ab + 36b
2
S o l u t i o n :
We have:
( )
( )
( )
49a
2
+84ab +36b
2
= (7a)
2
+2 ×7a ×6b +(6b)
2
= (7a +6b)
2
? 49a
2
+84ab +36b
2
= (7a +6b)
2
Q u e s t i o n : 6 7
Factorise:
p
2
- 10p + 25
S o l u t i o n :
We have:
p
2
-10p +25 = p
2
-2 ×p ×5 +(5)
2
= (p -5)
2
? p
2
-10p +25 = (p -5)
2
Q u e s t i o n : 6 8
Factorise:
121a
2
- 88ab + 16b
2
S o l u t i o n :
We have:
121a
2
-88ab +16b
2
= (11a)
2
-2 ×11a ×4b +(4b)
2
= (11a -4b)
2
? 121a
2
-88ab +16b
2
= (11a -4b)
2
Q u e s t i o n : 6 9
Factorise:
1 - 6x + 9x
2
S o l u t i o n :
We have:
1 -6x +9x
2
= 9x
2
-6x +1
= (3x)
2
-2 ×3x ×1 +(1)
2
= (3x -1)
2
? 1 -6x +9x
2
= (3x -1)
2
Q u e s t i o n : 7 0
Factorise:
9y
2
- 12y + 4
S o l u t i o n :
We have:
9y
2
-12y +4 = (3y)
2
-2 ×3y ×2 +(2)
2
= (3y -2)
2
? 9y
2
-12y +4 = (3y -2)
2
Q u e s t i o n : 7 1
Factorise:
16x
2
- 24x + 9
S o l u t i o n :
We have:
16x
2
-24x +9 = (4x)
2
-2 ×4x ×3 +(3)
2
= (4x -3)
2
? 16x
2
-24x +9 = (4x -3)
2
Q u e s t i o n : 7 2
Factorise:
m
2
- 4mn + 4n
2
S o l u t i o n :
We have:
m
2
-4mn +4n
2
= m
2
-2 ×m ×2n +(2n)
2
= (m -2n)
2
? m
2
-4mn +4n
2
= (m -2n)
2
Q u e s t i o n : 7 3
Factorise:
a
2
b
2
- 6abc + 9c
2
S o l u t i o n :
We have:
a
2
b
2
-6abc +9c
2
= (ab)
2
-2 ×ab ×3c +(3c)
2
= (ab -3c)
2
Q u e s t i o n : 7 4
Factorise:
m
4
+ 2m
2
n
2
+ n
4
S o l u t i o n :
We have:
m
4
+2m
2
n
2
+n
4
= m
2
2
+2 ×m
2
×n
2
+ n
2
2
= m
2
+n
2
2
? m
4
+2m
2
n
2
+n
4
= m
2
+n
2
2
( ) ( )
( )
( )
Q u e s t i o n : 7 5
Factorise:
(l + m)
2
- 4lm
S o l u t i o n :
We have:
(l +m)
2
-4lm = l
2
+m
2
+2lm -4lm
= l
2
+m
2
+2lm -4lm = l
2
+m
2
-2lm = (l)
2
+(m)
2
-2 ×l ×m = (l -m)
2
? (l +m)
2
-4lm = (l -m)
2
Q u e s t i o n : 7 6
Factorise:
x
2
+ 5x + 6
S o l u t i o n :
The given expression is x
2
+ 5x + 6. Find two numbers that follow the conditions given below: Sum = 5 Product = 6Clearly, the numbers are 3 and 2. x
2
+ 5x + 6 = x
2
+ 3x + 2x + 6
Q u e s t i o n : 7 7
Factorise:
y
2
+ 10y + 24
S o l u t i o n :
The given expression is y
2
+ 10y + 24. Find two numbers that follow the conditions given below: Sum = 10 Product = 24Clearly, the numbers are 6 and 4. y
2
+ 10y + 24 = y
2
+ 6y + 4y
Q u e s t i o n : 7 8
Factorise:
z
2
+ 12z + 27
S o l u t i o n :
The given expression is z
2
+ 12z + 27. Find two numbers that follow the conditions given below: Sum = 12 Product = 27Clearly, the numbers are 9 and 3. z
2
+ 12z + 27 = z
2
+ 9z + 3z
Q u e s t i o n : 7 9
Factorise:
p
2
+ 6p + 8
S o l u t i o n :
The given expression is p
2
+ 6p + 8. Find two numbers that follow the conditions given below: Sum = 6 Product = 8Clearly, the numbers are 4 and 2. p
2
+ 6p + 8 = p
2
+ 4p + 2p +8
Q u e s t i o n : 8 0
Factorise:
x
2
+ 15x + 56
S o l u t i o n :
The given expression is x
2
+ 15x + 56. Find two numbers that follow the conditions given below: Sum = 15 Product = 56Clearly, the numbers are 8 and 7. x
2
+ 15x + 56 = x
2
+ 8x + 7x
Q u e s t i o n : 8 1
Factorise:
y
2
+ 19y + 60
S o l u t i o n :
The given expression is y
2
+ 19y + 60. Find two numbers that follow the conditions given below: Sum = 19 Product = 60Clearly, the numbers are 15 and 4. y
2
+ 19y + 60 = y
2
+ 15y + 4
Q u e s t i o n : 8 2
Factorise:
x
2
+ 13x + 40
S o l u t i o n :
The given expression is x
2
+ 13x + 40. Find two numbers that follow the conditions given below: Sum = 13 Product = 40Clearly, the numbers are 8 and 5. x
2
+ 13x + 40 = x
2
+ 8x + 5x
Q u e s t i o n : 8 3
Factorise:
q
2
- 10q + 21
S o l u t i o n :
The given expression is q
2
-10q + 21. Find two numbers that follow the conditions given below: Sum = -10 Product = 21Clearly, the numbers are -7 and -3. q
2
-10q + 21 = q
2
-7q -3q +
Q u e s t i o n : 8 4
Factorise:
p
2
+ 6p - 16
S o l u t i o n :
The given expression is p
2
+ 6p -16. Find two numbers that follow the conditions given below: Sum = 6 Product = -16Clearly, the numbers are 8 and -2. p
2
+ 6p -16 = p
2
+8p -2p -16
Q u e s t i o n : 8 5
Factorise:
x
2
- 10x + 24
S o l u t i o n :
The given expression is x
2
-10x +24. Find two numbers that follow the conditions given below: Sum = -10 Product = 24Clearly, the numbers are -6 and -4. x
2
-10x +24 = x
2
-6x -4x +24
( )
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RS Aggarwal Solutions: Exercise 7C - Factorisation Class 8 Questions
The "RS Aggarwal Solutions: Exercise 7C - Factorisation 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.
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The content of RS Aggarwal Solutions: Exercise 7C - Factorisation is prepared as per the latest Class 8 syllabus.
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