## RD Sharma Class 8 Solutions Chapter 7 - Factorization (Ex 7.8) Exercise 7.8 - Free PDF

## FAQs on RD Sharma Class 8 Solutions Chapter 7 - Factorization (Ex 7.8) Exercise 7.8

**1. Finding the common factors of the given terms.**

(i) 12x, 36

(ii) 2y, 22xy

(iii) 14 pq, 28p2q2

(iv) PQx, 3x2, 4

(v) 6 abc, 24ab2, 12aABC

(vi) 16 x3, – 4x2, 32 x

(vii) 1 pq, 20qr, 30 rp PQ

(viii) 3x2y3, 10x3y2, 6x22z

(i) Factors of 12x and 36

12x = 2×2×3×x

36 = 2×2×3×3

Common factors of 12x and 36 are 2, 2, 3

and , 2×2×3 = 12

(ii) Factors of 2y and 22xy

2y = 2×y

22xy = 2×11×x×y

Common factors of 2y and 22xy are 2, y

and ,2×y = 2y

(iii) Factors of 14pq and 28p^{2}q

14pq = 2x7xpxq

28p^{2}q = 2x2x7xpxpxq

Common factors of 14 pq and 28 p^{2}q aPQ 2, 7 , p , q and, 27xpq = 14pq

(iv) Factors of 2x, 3x^{2}and 4

2x = 2×x

3x^{2}= 3×x×x

4 = 2×2

Common factors of 2x, 3x^{2}, and 4 are 1.

(v) Factors of 6abc, 24ab^{2}, and 12a^{2}b

6abc = 2×3×a×b×c

24ab^{2} = 2×2×2×3×a×b×b

12 a^{2} b = 2×2×3×a×a×b

Common factors of 6 ABC, 24ab^{2}, and 12a^{2}b are 2, 3, a, b and, 2×3×a×b = 6ab

(vi) Factors of 16x^{3}, -4x^{2}and 32x

16x^{3 }= 2×2×2×2×x×x×x

– 4x^{2} = -1×2×2×x×x

32x = 2×2×2×2×2×x

Common factors of 16 x^{3}, – 4x^{2}, and 32x are 2,2, x

and, 2×2×x = 4x

(vii) Factors of 10 PQ, 20qr and 30rp

10 pq = 2×5×p×q

20q, r = 2×2×5×q×r

30rp= 2×3×5×r×p

Common factors of 10 PQ, 20qr, and 30rp are 2, 5

and, 2×5 = 10

(viii) Factors of 3x^{2}y^{3}, 10x^{3}y^{2} and 6x^{2}y^{2}z

3x^{2}y^{3} = 3×x×x×y×y×y

10x^{3}y^{2} = 2×5×x×x×x×y×y

6x^{2}y^{2}z = 3×2×x×x×y×y×z

Common factors of 3x^{2}y^{3}, 10x^{3}y^{2} and 6x^{2}y^{2}z are x^{2}, y^{2} , x^{2}×y^{2 }= x^{2}y^{2 }

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**4. What are the steps to be followed when each term of the given algebraic expression contains a common monomial?**

Step 1:Find the greatest monomial factor which can divide each term of the given expression.

Step 2: Divide each term by the common monomial factor determined in step 1 to find the quotient.

Step 3: Write the given expression as a product of the common monomial factor and the quotient of name in step 2.

**5. What is the process of factorization?**

Step 1: Arrange the terms of the algebraic expressions in groups such that all the groups have a common factor.

Step 2: Factorize each group.

Step 3: Divide each group by Common Factor to find the quotient.

Step 4: Write the given expression as the product of the common factor and the quotient option obtained in step 3.