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

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Last updated date: 04th Mar 2024
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IVSAT 2024

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

Download free PDF of RD Sharma Class 8 solutions Chapter 7 - factorization  Exercise 7.8 solved by expert mathematics teachers on vedantu.com. All questions of Chapter  7 - factorization Exercise 7.8 with solutions for RD Sharma are available to help you to revise the complete syllabus and score good marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams. Vedantu is a platform that provides free as well as other study materials for students. Science students who are looking for NCERT solutions will also find it curated by our master teachers helpful. 

Introduction to the Chapter

Factorization is a process of reverse multiplication. Just like numbers, algebraic expressions can also be expressed as the product of factors, which may be numbered, algebraic variables are algebraic expressions. For  example 5x (X + 3) = 5×X×(X+3) . The factors 5 X and X + 3 cannot be further expressed as a product of factors. Hence, they are called irreducible factors. Factorization is the process of finding two or more expressions whose product is the given expression. 


Contents of the Chapter 

• Factors of algebraic expressions 

• Factorisation by grouping and regrouping 

• Factorisation using identities 


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The benefits of NCERT maths books and solutions for CBSE board exams are given  below: 

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  • The NCERT books provide a variety of solved examples, which help students in the understanding of concepts clearly and can well prepare for their  CBSE board exams. 

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, 6x22

(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 28p2

14pq = 2x7xpxq 

28p2q = 2x2x7xpxpxq 

Common factors of 14 pq and 28 p2q aPQ 2, 7 , p , q and, 27xpq = 14pq 


(iv) Factors of 2x, 3x2and 4 

2x = 2×x 

3x2= 3×x×x 

4 = 2×2 

Common factors of 2x, 3x2, and 4 are 1. 


(v) Factors of 6abc, 24ab2, and 12a2

6abc = 2×3×a×b×c 

24ab2 = 2×2×2×3×a×b×b 

12 a2 b = 2×2×3×a×a×b 

Common factors of 6 ABC, 24ab2, and 12a2b are 2, 3, a, b and, 2×3×a×b = 6ab 


(vi) Factors of 16x3, -4x2and 32x 

16x3 = 2×2×2×2×x×x×x 

– 4x2 = -1×2×2×x×x 

32x = 2×2×2×2×2×x 

Common factors of 16 x3, – 4x2, 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 3x2y3, 10x3y2 and 6x2y2

3x2y3 = 3×x×x×y×y×y 

10x3y2 = 2×5×x×x×x×y×y 

6x2y2z = 3×2×x×x×y×y×z 

Common factors of 3x2y3, 10x3y2 and 6x2y2z are x2, y2 , x2×y2 = x2y2 

2. How are NCERT books for the students of 8th standard?

NCERT books are extremely useful for the CBSE students as these study materials cover the entire CBSE curriculum and primarily focus on fundamentals to help the students to build a strong foundation for their next level of education.  NCERT books are comprehensive, skilled in their sense, and also very helpful study material. These NCERT books hold great advantages for the students in their board exam preparations. As per the topper’s advice, the NCERT books are the best study material. 

3. Does NCERT provide solutions to the students appearing for the exam?

During the exam preparation, students might be confused about which books to refer to amongst the plenty of options available in the market. Some of the students waste their time selecting the right study materials and finally end up choosing the wrong study material. For them, NCERT proves to be the best study material for the entire preparation of the examination.

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.