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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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)
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