## RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4

**Other Exercises**

- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.1
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.2
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.3
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9

**Factorize each of the following expressions :**

**Question 1.**

**qr-pr + qs – ps**

**Solution:**

qr- pr + qs-ps

Arranging in suitable groups = r(q-p) +s (q-p) {(q – p) is common}

= (q-p) (r + s)

**Question 2.**

**p ^{2}q -pr^{2}-pq + r^{2}**

**Solution:**

p

^{2}q -pr

^{2}-pq + r2

= p

^{2}q -pq-pr

^{2}+ r

^{2}(Arranging in group)

= pq(p- 1)-r

^{2}(p-1) {(p – 1) is common}

= (p – 1) (pq – r

^{2})

**Question 3.
**

**1 + x + xy + x**

^{2}y**Solution:**

1 + x + xy + x 2y

= 1 (1 + x) +xy (1 +x)

= (1 + x) (1 + xy) {(1 + x) is common}

**Question 4.**

**ax + ay – bx – by**

**Solution:**

ax + ay – bx – by

= a (x + y) – b (x + y) {(x + y) is coinmon}

= (x+y) (a- b)

**Question 5.**

**xa ^{2} + xb^{2} -ya^{2} – yb^{2}**

**Solution:**

xa

^{2}+ xb

^{2}– ya

^{2}– yb

^{2 }= x (a

^{2}+ b

^{2}) -y (a

^{2}+ b

^{2}) {(a

^{2}+ b

^{2}) is common}

= {a

^{2}+ b

^{2}) (x -y)

**Question 6.
**

**x**

^{2}+ xy + xz + yz**Solution:**

x

^{2}+ xy + xz + yz

= x (x + y) + z(x + y) {(x + y) is common}

= (x + y) (x + z)

**Question 7.
**

**2ax + bx + 2ay**

*+*by**Solution:**

2ax + bx + 2ay + by

= x {2a + b) + y (2a + b) {(2a + b) is common}

= (2a + b) (x + y)

**Question 8.
**

**ab- by- ay +y**

^{2 }

**Solution:**

ab – by – ay + y

^{2 }= b(a-y)-y(a-y) {(a -y) is common}

= (a-y) (b – y)

**Question 9.
**

**axy + bcxy -az- bcz**

**Solution:**

axy + bcxy – az – bcz

= xy (a + bc) – z (a + bc) {(a + bc) is common}

= (a + bc) (xy – z)

**Question 10.
**

**lm**

^{2}– mn^{2}*– l*m + n^{2 }

**Solution:**

lm

^{2}– mn

^{2}– lm + n

^{2 }= m (lm – n

^{2})- 1 (lm – n

^{2}) {(lm – n

^{2}) is common}

= (lm – n

^{2}) (m – 1)

**Question 11.
**

**x**

^{3 }– y^{2 }+ x – x^{2}y^{2 }

**Solution:**

x

^{3}-y

^{2}+ x – x

^{2}y

^{2 }⇒ x

^{3}+ x – x

^{2}y

^{2}– y

^{2 }= x(x

^{2}+ 1)-y

^{2}(x

^{2}+ 1) {(x

^{2}+ 1) is common}

= (x

^{2}+ 1) (x -y

^{2})

**Question 12.
**

**6xy +**

*6 –*9y – 4x**Solution:**

6xy + 6 – 9y – 4x

= 6 xy – 4x – 9y + 6

= 2x (3y – 2) – 3 (3y – 2) {(3y – 2) is common}

= (3y-2) (2x – 3)

**Question 13.
**

*x*2ax – 2ab + bx^{2}–**Solution:**

x

^{2}– 2ax – 2ab + bx

⇒ x

^{2}– 2ax + bx – 2ab

= x (x – 2a) + b (x – 2a) {(x – 2a) is common}

= (x – 2a) (x + b)

**Question 14.
**

**x**

^{3}– 2x^{2}y + 3xy^{2}– 6y^{3 }

**Solution:**

x

^{3}– 2x

^{2}y + 3xy

^{2}– 6y

^{3 }= x

^{2}(x – 2y) + 3y

^{2}(x – 2y) {(x – 2y) is common}

= (x – 2y) (x

^{2}+ 3y

^{2})

**Question 15.
**

**abx**

^{2}*+*(ay – b) x-y**Solution:**

abx

^{2}+ (ay – b) x-y

= abx

^{2}+ ayx – bx -y

^{ }= ax (bx + y) – 1 (bx + y) {(bx +y) is common}

= (bx + y) (ax – 1)

**Question 16.
**

**(ax + by)**

^{2}+ (bx – ay)^{2 }

**Solution:**

(ax + by)

^{2}+ (bx – ay)

^{2 }= a

^{2}x

^{2}+ b

^{2}y

^{2}+ 2abxy + b

^{2}x

^{2}+ a

^{2}y

^{2}– 2abxy

= a

^{2}x

^{2}+ b

^{2}y

^{2}+ b

^{2}x

^{2}+ a

^{2}y

^{2 }= a

^{2}x

^{2}+ b

^{2}x

^{2}+ a

^{2}y

^{2}+ by

^{2 }= x

^{2}(a

^{2}+ b

^{2}) + y

^{2}(a

^{2}+ b

^{2}) {(a

^{2}+ b

^{2}) is common}

*=*(a

^{2}+ b

^{2})

*(x*y

^{2}+^{2})

**Question 17.
**

*16*(a*–*b)^{3}*-24*(a- b)^{2 }

**Solution:**

16 (a – b)

^{3}-24 (a- b)

^{2}

HCF of 16, 24 = 8

and HCF of (a – b)

^{3}, (a – b)

^{2}= (a – b)

^{2 }∴16 (a – b)

^{3}– 24 (a – b)

^{2 }= 8 (a-b)

^{2}{2 (a-b)- 3}

{8 (a – b)

^{2}is common}

= 8 (a – b)

^{2}(2a – 2b – 3)

**Question 18.
**

**ab (x**

^{2}+ 1) + x (a^{2}+ b^{2})**Solution:**

ab (x

^{2}+ 1) + x (a

^{2}+ b

^{2})

= abx

^{2}+ ab + a

^{2}x + b

^{2}x

= abx

^{2}+ b

^{2}x + a

^{2}x + ab

= bx (ax + b) + a (ax + b) {(ax + b) is common}

= (ax + b) (bx + a)

**Question 19.
**

**a**

^{2}x^{2}*+ (*ax^{2}*+ 1)*x + a**Solution:**

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

= ax

^{2}(x + a) + 1 (x + a) {(x + a) is common}

= (x + a) (ax

^{2}+ 1)

**Question 20.
**

**a(a- 2b -c) + 2bc**

**Solution:**

a(a- 2b -c) + 2bc

**= a**

^{2}– 2ab -ac +2bc

**= a (a – 2b) – c (a – 2b) {(a – 2b) is common}**

= (a – 2b) (a – c)

**Question 21.
**

**a (a + b – c)- bc**

**Solution:**

a (a + b – c) – bc

= a

^{2}+ ab – ac – bc

= a (a + b) – c (a + b) {(a + b) is common}

= (a + b) (a – c)

**Question 22.
**

**x**

^{2}– 11xy – x +11y**Solution:**

x

^{2}– 11xy-x + 11y

= x

^{2}-x – 11 xy + 11 y

= x (x – 1) – 11y (x – 1) {(x – 1) is common}

= (x- 1) (x- 11y)

**Question 23.
**

**ab – a – b +**

**1****Solution:**

ab – a-b + 1

= a (b – 1) – 1 (b – 1) {(b – 1) is common}

= (b – 1) (a – 1)

**Question 24.
**

**x**

^{2}+ y – xy – x**Solution:**

x

^{2}+ y – xy – x

= x

^{2}– x- xy + y

= x (x – 1) – y (x – 1) {(x – 1) is common}

*=*(x-

*1)*(x-y)

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4 are helpful to complete your math homework.

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