Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Factorization - Exercise 7.4
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Page 1
Q u e s t i o n : 5 0
Factorize each of the following expressions:
qr - pr + qs - ps
S o l u t i o n :
qr-pr+qs -ps = (qr-pr)+(qs -ps) [Grouping the expressions] = r(q -p)+s(q -p) = (r+s)(q -p) [Taking (q -p) as the common factor]
Q u e s t i o n : 5 1
Factorize each of the following expressions:
p
2
q - pr
2
- pq + r
2
S o l u t i o n :
p
2
q -pr
2
-pq +r
2
= p
2
q -pq + r
2
-pr
2
Grouping the expressions = pq p -1 +r
2
1 -p = pq p -1 -r
2
p -1 ? 1 -p = - p -1 = pq -r
2
p -1 Taking p -1 as the commo
Q u e s t i o n : 5 2
Factorize each of the following expressions:
1 + x + xy + x
2
y
S o l u t i o n :
1 +x +xy +x
2
y = 1 +x + xy +x
2
y Grouping the expressions = 1 +x +xy 1 +x = 1 +xy 1 +x Taking 1 +x as the common factor
Q u e s t i o n : 5 3
Factorize each of the following expressions:
ax + ay - bx - by
S o l u t i o n :
ax +ay -bx -by = (ax +ay)-(bx +by) [Grouping the expressions] = a(x +y)-b(x +y) = (a -b)(x +y) [Taking (x +y) as the common factor]
Q u e s t i o n : 5 4
Factorize each of the following expressions:
xa
2
+ xb
2
- ya
2
- yb
2
S o l u t i o n :
xa
2
+xb
2
-ya
2
-yb
2
= xa
2
+xb
2
- ya
2
+yb
2
Grouping the expressions = x a
2
+b
2
-y a
2
+b
2
= x -y a
2
+b
2
Taking a
2
+b
2
as the common factor
Q u e s t i o n : 5 5
Factorize each of the following expressions:
x
2
+ xy + xz + yz
S o l u t i o n :
x
2
+xy +xz +yz = x
2
+xy + xz +yz Grouping the expressions = x x +y +z x +y = x +z x +y Taking x +y as the common factor = x +y x +z
Q u e s t i o n : 5 6
Factorize each of the following expressions:
2ax + bx + 2ay + by
S o l u t i o n :
2ax +bx +2ay +by = (2ax +bx)+(2ay +by) [Grouping the expressions] = x(2a +b)+y(2a +b) = (x +y)(2a +b) [Taking (2a +b) as the common factor]
Q u e s t i o n : 5 7
Factorize each of the following expressions:
ab - by - ay + y
2
S o l u t i o n :
ab -by -ay +y
2
= ab -ay + y
2
-by Grouping the expressions = a b -y +y y -b = a b -y -y b -y ? y -b = - b -y = a -y b -y Taking b -y
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Page 2
Q u e s t i o n : 5 0
Factorize each of the following expressions:
qr - pr + qs - ps
S o l u t i o n :
qr-pr+qs -ps = (qr-pr)+(qs -ps) [Grouping the expressions] = r(q -p)+s(q -p) = (r+s)(q -p) [Taking (q -p) as the common factor]
Q u e s t i o n : 5 1
Factorize each of the following expressions:
p
2
q - pr
2
- pq + r
2
S o l u t i o n :
p
2
q -pr
2
-pq +r
2
= p
2
q -pq + r
2
-pr
2
Grouping the expressions = pq p -1 +r
2
1 -p = pq p -1 -r
2
p -1 ? 1 -p = - p -1 = pq -r
2
p -1 Taking p -1 as the commo
Q u e s t i o n : 5 2
Factorize each of the following expressions:
1 + x + xy + x
2
y
S o l u t i o n :
1 +x +xy +x
2
y = 1 +x + xy +x
2
y Grouping the expressions = 1 +x +xy 1 +x = 1 +xy 1 +x Taking 1 +x as the common factor
Q u e s t i o n : 5 3
Factorize each of the following expressions:
ax + ay - bx - by
S o l u t i o n :
ax +ay -bx -by = (ax +ay)-(bx +by) [Grouping the expressions] = a(x +y)-b(x +y) = (a -b)(x +y) [Taking (x +y) as the common factor]
Q u e s t i o n : 5 4
Factorize each of the following expressions:
xa
2
+ xb
2
- ya
2
- yb
2
S o l u t i o n :
xa
2
+xb
2
-ya
2
-yb
2
= xa
2
+xb
2
- ya
2
+yb
2
Grouping the expressions = x a
2
+b
2
-y a
2
+b
2
= x -y a
2
+b
2
Taking a
2
+b
2
as the common factor
Q u e s t i o n : 5 5
Factorize each of the following expressions:
x
2
+ xy + xz + yz
S o l u t i o n :
x
2
+xy +xz +yz = x
2
+xy + xz +yz Grouping the expressions = x x +y +z x +y = x +z x +y Taking x +y as the common factor = x +y x +z
Q u e s t i o n : 5 6
Factorize each of the following expressions:
2ax + bx + 2ay + by
S o l u t i o n :
2ax +bx +2ay +by = (2ax +bx)+(2ay +by) [Grouping the expressions] = x(2a +b)+y(2a +b) = (x +y)(2a +b) [Taking (2a +b) as the common factor]
Q u e s t i o n : 5 7
Factorize each of the following expressions:
ab - by - ay + y
2
S o l u t i o n :
ab -by -ay +y
2
= ab -ay + y
2
-by Grouping the expressions = a b -y +y y -b = a b -y -y b -y ? y -b = - b -y = a -y b -y Taking b -y
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Q u e s t i o n : 5 8
Factorize each of the following expressions:
axy + bcxy - az - bcz
S o l u t i o n :
axy +bcxy -az -bcz = (axy +bcxy)-(az +bcz) [Grouping the expressions] = xy(a +bc)-z(a +bc) = (xy -z)(a +bc) [Taking (a +bc) as the common factor]
Q u e s t i o n : 5 9
Factorize each of the following expressions:
lm
2
- mn
2
- lm + n
2
S o l u t i o n :
lm
2
-mn
2
-lm +n
2
= lm
2
-lm + n
2
-mn
2
Regrouping the expressions = lm m -1 +n
2
1 -m = lm m -1 -n
2
m -1 ? 1 -m = - m -1
Q u e s t i o n : 6 0
Factorize each of the following expressions:
x
3
- y
2
+ x - x
2
y
2
S o l u t i o n :
x
3
-y
2
+x -x
2
y
2
= x
3
+x - x
2
y
2
+y
2
Regrouping the expressions = x x
2
+1 -y
2
x
2
+1 = x -y
2
x
2
+1 Taking x
2
+1 as the common factor
Q u e s t i o n : 6 1
Factorize each of the following expressions:
6xy + 6 - 9y - 4x
S o l u t i o n :
6xy +6 -9y -4x = (6xy -4x)+(6 -9y) [Regrouping the expressions] = 2x(3y -2)+3(2 -3y) = 2x(3y -2)-3(3y -2) [ ? (2 -3y) = -(3y -2)] = (2
Q u e s t i o n : 6 2
Factorize each of the following expressions:
x
2
- 2ax - 2ab + bx
S o l u t i o n :
x
2
-2ax -2ab +bx = x
2
-2ax + bx -2ab Regrouping the expressions = x x -2a +b x -2a = x +b x -2a Taking x -2a as the common factor = x -2a x +b
Q u e s t i o n : 6 3
Factorize each of the following expressions:
x
3
- 2x
2
y + 3xy
2
- 6y
3
S o l u t i o n :
x
3
- 2x
2
y + 3xy
2
- 6y
3
= x
3
-2x
2
y + 3xy
2
-6y
3
Grouping the expressions = x
2
x -2y +3y
2
x -2y = x
2
+3y
2
x -2y Taking x -2y as the common factor
Q u e s t i o n : 6 4
Factorize each of the following expression:
abx
2
+ (ay - b) x - y
S o l u t i o n :
abx
2
+ ay -b x -y = abx
2
+axy -bx -y = abx
2
-bx + axy -y Regrouping the expressions = bx ax -1 +y ax -1 = bx
Q u e s t i o n : 6 5
Factorize each of the following expression:
(ax + by)
2
+ (bx - ay)
2
S o l u t i o n :
ax +by)
2
+ bx -ay)
2
= a
2
x
2
+2abxy +b
2
y
2
+b
2
x
2
-2abxy +a
2
y
2
= a
2
x
2
+b
2
y
2
+b
2
x
2
+a
2
y
2
= a
2
x
2
+a
2
y
2
+ b
2
x
2
+b
2
y
2
Regrouping the ex
Q u e s t i o n : 6 6
Factorize each of the following expression:
16(a - b)
3
- 24 (a - b)
2
S o l u t i o n :
16 a -b)
3
-24 a -b)
2
= 8 a -b)
2
2 a -b -3 Taking 8 a -b)
2
as the common factor = 8 a -b)
2
2a -2b -3
Q u e s t i o n : 6 7
Factorize each of the following expression:
ab(x
2
+ 1) + x(a
2
+ b
2
)
S o l u t i o n :
ab x
2
+1 +x a
2
+b
2
= abx
2
+ab +a
2
x +b
2
x = abx
2
+a
2
x + b
2
x +ab Regrouping the expressions = ax bx +a +b bx +a
Q u e s t i o n : 6 8
Factorize each of the following expression:
a
2
x
2
+ (ax
2
+ 1)x + a
S o l u t i o n :
a
2
x
2
+ ax
2
+1 x +a = a
2
x
2
+ax
3
+x +a = ax
3
+a
2
x
2
+ x +a Regrouping the expressions = ax
2
x +a + x +a = ax
Q u e s t i o n : 6 9
Factorize each of the following expression:
a(a - 2b - c) + 2bc
S o l u t i o n :
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Page 3
Q u e s t i o n : 5 0
Factorize each of the following expressions:
qr - pr + qs - ps
S o l u t i o n :
qr-pr+qs -ps = (qr-pr)+(qs -ps) [Grouping the expressions] = r(q -p)+s(q -p) = (r+s)(q -p) [Taking (q -p) as the common factor]
Q u e s t i o n : 5 1
Factorize each of the following expressions:
p
2
q - pr
2
- pq + r
2
S o l u t i o n :
p
2
q -pr
2
-pq +r
2
= p
2
q -pq + r
2
-pr
2
Grouping the expressions = pq p -1 +r
2
1 -p = pq p -1 -r
2
p -1 ? 1 -p = - p -1 = pq -r
2
p -1 Taking p -1 as the commo
Q u e s t i o n : 5 2
Factorize each of the following expressions:
1 + x + xy + x
2
y
S o l u t i o n :
1 +x +xy +x
2
y = 1 +x + xy +x
2
y Grouping the expressions = 1 +x +xy 1 +x = 1 +xy 1 +x Taking 1 +x as the common factor
Q u e s t i o n : 5 3
Factorize each of the following expressions:
ax + ay - bx - by
S o l u t i o n :
ax +ay -bx -by = (ax +ay)-(bx +by) [Grouping the expressions] = a(x +y)-b(x +y) = (a -b)(x +y) [Taking (x +y) as the common factor]
Q u e s t i o n : 5 4
Factorize each of the following expressions:
xa
2
+ xb
2
- ya
2
- yb
2
S o l u t i o n :
xa
2
+xb
2
-ya
2
-yb
2
= xa
2
+xb
2
- ya
2
+yb
2
Grouping the expressions = x a
2
+b
2
-y a
2
+b
2
= x -y a
2
+b
2
Taking a
2
+b
2
as the common factor
Q u e s t i o n : 5 5
Factorize each of the following expressions:
x
2
+ xy + xz + yz
S o l u t i o n :
x
2
+xy +xz +yz = x
2
+xy + xz +yz Grouping the expressions = x x +y +z x +y = x +z x +y Taking x +y as the common factor = x +y x +z
Q u e s t i o n : 5 6
Factorize each of the following expressions:
2ax + bx + 2ay + by
S o l u t i o n :
2ax +bx +2ay +by = (2ax +bx)+(2ay +by) [Grouping the expressions] = x(2a +b)+y(2a +b) = (x +y)(2a +b) [Taking (2a +b) as the common factor]
Q u e s t i o n : 5 7
Factorize each of the following expressions:
ab - by - ay + y
2
S o l u t i o n :
ab -by -ay +y
2
= ab -ay + y
2
-by Grouping the expressions = a b -y +y y -b = a b -y -y b -y ? y -b = - b -y = a -y b -y Taking b -y
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Q u e s t i o n : 5 8
Factorize each of the following expressions:
axy + bcxy - az - bcz
S o l u t i o n :
axy +bcxy -az -bcz = (axy +bcxy)-(az +bcz) [Grouping the expressions] = xy(a +bc)-z(a +bc) = (xy -z)(a +bc) [Taking (a +bc) as the common factor]
Q u e s t i o n : 5 9
Factorize each of the following expressions:
lm
2
- mn
2
- lm + n
2
S o l u t i o n :
lm
2
-mn
2
-lm +n
2
= lm
2
-lm + n
2
-mn
2
Regrouping the expressions = lm m -1 +n
2
1 -m = lm m -1 -n
2
m -1 ? 1 -m = - m -1
Q u e s t i o n : 6 0
Factorize each of the following expressions:
x
3
- y
2
+ x - x
2
y
2
S o l u t i o n :
x
3
-y
2
+x -x
2
y
2
= x
3
+x - x
2
y
2
+y
2
Regrouping the expressions = x x
2
+1 -y
2
x
2
+1 = x -y
2
x
2
+1 Taking x
2
+1 as the common factor
Q u e s t i o n : 6 1
Factorize each of the following expressions:
6xy + 6 - 9y - 4x
S o l u t i o n :
6xy +6 -9y -4x = (6xy -4x)+(6 -9y) [Regrouping the expressions] = 2x(3y -2)+3(2 -3y) = 2x(3y -2)-3(3y -2) [ ? (2 -3y) = -(3y -2)] = (2
Q u e s t i o n : 6 2
Factorize each of the following expressions:
x
2
- 2ax - 2ab + bx
S o l u t i o n :
x
2
-2ax -2ab +bx = x
2
-2ax + bx -2ab Regrouping the expressions = x x -2a +b x -2a = x +b x -2a Taking x -2a as the common factor = x -2a x +b
Q u e s t i o n : 6 3
Factorize each of the following expressions:
x
3
- 2x
2
y + 3xy
2
- 6y
3
S o l u t i o n :
x
3
- 2x
2
y + 3xy
2
- 6y
3
= x
3
-2x
2
y + 3xy
2
-6y
3
Grouping the expressions = x
2
x -2y +3y
2
x -2y = x
2
+3y
2
x -2y Taking x -2y as the common factor
Q u e s t i o n : 6 4
Factorize each of the following expression:
abx
2
+ (ay - b) x - y
S o l u t i o n :
abx
2
+ ay -b x -y = abx
2
+axy -bx -y = abx
2
-bx + axy -y Regrouping the expressions = bx ax -1 +y ax -1 = bx
Q u e s t i o n : 6 5
Factorize each of the following expression:
(ax + by)
2
+ (bx - ay)
2
S o l u t i o n :
ax +by)
2
+ bx -ay)
2
= a
2
x
2
+2abxy +b
2
y
2
+b
2
x
2
-2abxy +a
2
y
2
= a
2
x
2
+b
2
y
2
+b
2
x
2
+a
2
y
2
= a
2
x
2
+a
2
y
2
+ b
2
x
2
+b
2
y
2
Regrouping the ex
Q u e s t i o n : 6 6
Factorize each of the following expression:
16(a - b)
3
- 24 (a - b)
2
S o l u t i o n :
16 a -b)
3
-24 a -b)
2
= 8 a -b)
2
2 a -b -3 Taking 8 a -b)
2
as the common factor = 8 a -b)
2
2a -2b -3
Q u e s t i o n : 6 7
Factorize each of the following expression:
ab(x
2
+ 1) + x(a
2
+ b
2
)
S o l u t i o n :
ab x
2
+1 +x a
2
+b
2
= abx
2
+ab +a
2
x +b
2
x = abx
2
+a
2
x + b
2
x +ab Regrouping the expressions = ax bx +a +b bx +a
Q u e s t i o n : 6 8
Factorize each of the following expression:
a
2
x
2
+ (ax
2
+ 1)x + a
S o l u t i o n :
a
2
x
2
+ ax
2
+1 x +a = a
2
x
2
+ax
3
+x +a = ax
3
+a
2
x
2
+ x +a Regrouping the expressions = ax
2
x +a + x +a = ax
Q u e s t i o n : 6 9
Factorize each of the following expression:
a(a - 2b - c) + 2bc
S o l u t i o n :
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( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ( ) ]
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( ) ( ) ( ) [ ] ( ) ( ) (
( ( ( ) ( ) [
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( ) ( ) ( ) [ ] ( ) ( ) ( ) (
a a -2b -c +2bc = a
2
-2ab -ac +2bc = a
2
-ac + 2bc -2ab Regrouping the terms = a a -c +2b c -a = a a -c -2b
Q u e s t i o n : 7 0
Factorize each of the following expression:
a(a + b - c) - bc
S o l u t i o n :
a a +b -c -bc = a
2
+ab -ac -bc = a
2
-ac + ab -bc Regrouping the expressions = a a -c +b a -c = a +b a -c Taki
Q u e s t i o n : 7 1
Factorize each of the following expression:
x
2
- 11xy - x + 11y
S o l u t i o n :
x
2
-11xy -x +11y = x
2
-x + 11y -11xy Regrouping the expressions = x x -1 +11y 1 -x = x x -1 -11y x -1 ? 1 -x = - x -1
Q u e s t i o n : 7 2
Factorize each of the following expression:
ab - a - b + 1
S o l u t i o n :
ab -a -b +1 = (ab -b)+(1 -a) [Regrouping the expressions] = b(a -1)+(1 -a) = b(a -1)-(a -1) [ ? (1 -a) = -(a -1)] = (a -1)(b -1) [Taking out the c
Q u e s t i o n : 7 3
Factorize each of the following expression:
x
2
+ y - xy - x
S o l u t i o n :
x
2
+y -xy -x = x
2
-xy + y -x Regrouping the expressions = x x -y + y -x = x x -y - x -y ? y -x = - x -y = x -1 x -y
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Document Description: Factorization - Exercise 7.4 for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
The notes and questions for Factorization - Exercise 7.4 have been prepared according to the Class 8 exam syllabus. Information about Factorization - Exercise 7.4 covers topics
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Full syllabus notes, lecture & questions for Factorization - Exercise 7.4 | 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
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Additional Information about Factorization - Exercise 7.4 for Class 8 Preparation
Factorization - Exercise 7.4 Free PDF Download
The Factorization - Exercise 7.4 is an invaluable resource that delves deep into the core of the Class 8 exam.
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Importance of Factorization - Exercise 7.4
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Factorization - Exercise 7.4 Notes
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Factorization - Exercise 7.4 Class 8 Questions
The "Factorization - Exercise 7.4 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
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The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
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The content of Factorization - Exercise 7.4 is prepared as per the latest Class 8 syllabus.
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