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

RD Sharma Solutions for Class 9 Mathematics Chapter 5 Exercise 5.3 Factorization of Algebraic Expressions are provided here. These exercise solutions are helpful for practising factorization by using the formulae for the cube of a binomial. Students can enhance their understanding 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 factorization of algebraic expressions, which are expressible in the form (x + y)³ or (x – y)³.

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Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 5 Factorization of Algebraic Expressions Exercise 5.3 Page Number 5.17

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 – 27y³ – 225x²y + 135xy²

Solution:

125x³ – 27y³ – 225x²y + 135xy²

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

Using: a³ − b³ − 3a²b + 3ab² = (a−b)³

= (5x − 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 + 3×(2x)²×3y + 3×(2x)(3y)²

Which is similar to a³ + b³ + 3a²b + 3ab² = (a + b) ³]

Here a = 2x and b = 3y

= (2x+3y)³

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

Question 5: Factorize a³ − 3a²b + 3ab² − b³ + 8

Solution:

a³ − 3a²b + 3ab² − b³ + 8

Using: a³ − b³ − 3a²b + 3ab² = (a−b)³

= (a−b)³ + 2³

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

=(a−b+2)((a−b)²−(a−b)×2 + 2²)

=(a−b+2)(a²+b²−2ab−2(a−b)+4)

=(a−b+2)(a²+b²−2ab−2a+2b+4)

a³ − 3a²b + 3ab² − b³ + 8 =(a−b+2)(a²+b²−2ab−2a+2b+4)

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

RD Sharma Solutions for Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise 5.3 are based on the following topic:

• Factorization 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)