Given that, a + 1 a 3 We know that, x + y 3 = x 3 + y 3 + 3 x y x + y Here, x = a , y = 1 a Hence, a + 1 a 3 = a 3 + 3 a + 3 a + 1 a 3

Given that, 2 a - 1 2 a 3 We know that, a - b 3 = a 3 - b 3 - 3 a b a - b Here, a = 2 a , b = 1 2 a Hence, 2 a - 1 2 a 3 = 2 a 3 - 3 2 a 2 1 2 a + 3 2 a 1 2 a 2 - 1 2 a 3 = 8 a 3 - 6 a + 3 2 a - 1 8 a 3 Required expression is 8 a 3 - 6 a + 3 2 a - 1 8 a 3

Find the cube of ( 2 x + 1 x )

Given that, ( 2 x + 1 x ) We know that, a + b 3 = a 3 + b 3 + 3 a b a + b Here, a = 2 x , b = 1 x Hence, 2 x + 1 x 3 = 2 x 3 + 3 2 x 2 1 x + 3 2 x 1 x 2 + 1 x 3 = 8 x 3 + 12 x + 6 x + 1 x 3

Find the cube of x - 1 2

Given that, x - 1 2 We know that, a - b 3 = a 3 - b 3 - 3 a b a - b Here, a = x , b = 1 2 Hence, x - 1 2 3 = x 3 - 3 x 2 1 2 + 3 x 1 2 2 - 1 2 = x 3 - 3 2 x 2 + 3 4 x - 1 8

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Concise Mathematics Middle School Class 8>Chapter 12 - Identities>EXERCISE 12(B)

R K Bansal Solutions for Chapter: Identities, Exercise 2: EXERCISE 12(B)

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Chapter: Identities, Exercise 2: EXERCISE 12(B)

Attempt the free practice questions on Chapter 12: Identities, Exercise 2: EXERCISE 12(B) with hints and solutions to strengthen your understanding. Concise Mathematics Middle School Class 8 solutions are prepared by Experienced Embibe Experts.