# RD Sharma Solutions for Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise 5.3

RD Sharma Class 9 Mathematics Chapter 5 Exercise 5.3 Factorization of Algebraic Expressions is provided here. These exercise solutions are helpful to practice on factorization by using the formulae for the cube of a binomial. Students can enhance their knowledge quotient using the RD Sharma Solutions Class 9 chapter 5 and also get a clear overview of the topics. In this exercise, students will study the factorisation of algebraic expressions which are expressible in the form (x + y)3 or (x – y)3.

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#### Exercise 5.3 Page No: 5.17

Question 1: Factorize 64a3 + 125b3 + 240a2b + 300ab2

Solution:

64a3 + 125b3 + 240a2b + 300ab2

= (4a)3 + (5b) 3 + 3(4a)2(5b) + 3(4a)(5b)2 , which is similar to a3 + b3 + 3a2b + 3ab2

We know that, a3 + b3 + 3a2b + 3ab2 = (a+b)3]

= (4a+5b)3

Question 2: Factorize 125x3 â€“ 27y3 â€“ 225x2y + 135xy2

Solution:

125x3 â€“ 27y3 â€“ 225x2y + 135xy2

Above expression can be written as (5x)3âˆ’(3y) 3âˆ’3(5x)2(3y) + 3(5x)(3y)2

Using: a3 âˆ’ b3 âˆ’ 3a2b + 3ab2 = (aâˆ’b)3

= (5x âˆ’ 3y)3

Question 3: Factorize 8/27 x3 + 1 + 4/3 x2 + 2x

Solution:

8/27 x3 + 1 + 4/3 x2 + 2x

Question 4: Factorize 8x3 + 27y3 + 36x2y + 54xy2

Solution:

8x3 + 27y3 + 36x2y + 54xy2

Above expression can be written as (2x)3 + (3y) 3 + 3Ã—(2x)2Ã—3y + 3Ã—(2x)(3y)2

Which is similar to aÂ³ + bÂ³ + 3aÂ²b + 3abÂ² = (a + b) Â³]

Here a = 2x and b = 3y

= (2x+3y)3

Therefore, 8x3 + 27y3 + 36x2y + 54xy2 = (2x+3y)3

Question 5: Factorize a3 âˆ’ 3a2b + 3ab2 âˆ’ b3 + 8

Solution:

a3 âˆ’ 3a2b + 3ab2 âˆ’ b3 + 8

Using: a3 âˆ’ b3 âˆ’ 3a2b + 3ab2 = (aâˆ’b)3

= (aâˆ’b)3 + 23

Again , Using: a3 + b3 =(a + b)(a2 â€“ ab + b2)]

=(aâˆ’b+2)((aâˆ’b)2âˆ’(aâˆ’b)Ã—2Â + 22)

=(aâˆ’b+2)(a2+b2âˆ’2abâˆ’2(aâˆ’b)+4)

=(aâˆ’b+2)(a2+b2âˆ’2abâˆ’2a+2b+4)

a3 âˆ’ 3a2b + 3ab2 âˆ’ b3 + 8 =(aâˆ’b+2)(a2+b2âˆ’2abâˆ’2a+2b+4)

## RD Sharma Solutions for Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise 5.3

RD Sharma SolutionsÂ Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise 5.3 is based on the following topic:

• Factorisation by using the formulae for the cube of a binomial

(x + y)3 = x3 + y3 + 3xy(x + y)

(x – y)3 = x3 – y3 – 3xy(x – y)