Find the product of 5 6 a 2 + 2 5 6 a 2 + 2 .

To find the product of 5 6 a 2 + 2 5 6 a 2 + 2 ⇒ 5 6 a 2 + 2 5 6 a 2 + 2 = 5 6 a 2 + 2 2 Using the algebraic identity, a + b 2 = a 2 + 2 a b + b 2 5 6 a 2 + 2 2 = 5 6 a 2 2 + 2 × 5 6 a 2 2 + 2 2 = 25 36 a 4 + 10 3 a 2 + 4 Thus, 5 6 a 2 + 2 5 6 a 2 + 2 = 25 36 a 4 + 10 3 a 2 + 4 .

Find the product of 1 3 x 2 - 9 1 3 x 2 - 9 .

Given, 1 3 x 2 - 9 1 3 x 2 - 9 By using the formula ( a - b ) 2 = a 2 - 2 a b + b 2 We get, 1 3 x 2 - 9 1 3 x 2 - 9 = 1 3 x 2 - 9 2 = 1 3 x 2 2 - 2 × 1 3 x 2 9 + 9 2 = 1 9 x 4 - 6 x 2 + 81 Thus, 1 3 x 2 - 9 1 3 x 2 - 9 = 1 9 x 4 - 6 x 2 + 81 .

Find the product of 1 2 y 2 - 1 3 y 1 2 y 2 - 1 3 y .

Given, 1 2 y 2 - 1 3 y 1 2 y 2 - 1 3 y By using the formula ( a - b ) 2 = a 2 - 2 a b + b 2 We get, 1 2 y 2 - 1 3 y 1 2 y 2 - 1 3 y = 1 2 y 2 - 1 3 y 2 = 1 2 y 2 2 - 2 × 1 2 y 2 1 3 y + 1 3 y 2 = 1 2 2 y 2 2 - y 2 1 3 y + 1 3 2 y 2 = 1 4 y 4 - 1 3 y 3 + 1 9 y 2 Thus, 1 2 y 2 - 1 3 y 1 2 y 2 - 1 3 y = 1 4 y 4 - 1 3 y 3 + 1 9 y 2 .

Find the product of 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 .

Given, 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 Using the algebraic identity, ( a + b ) ( a – b ) = a 2 – b 2 We get, 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 = 5 x 2 2 - 3 4 y 2 2 = 25 x 4 - 9 16 y 4 Thus, 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 = 25 x 4 - 9 16 y 4 .

Find the product of 4 x 5 - 5 y 3 4 x 5 + 5 y 3 .

Given, 4 x 5 - 5 y 3 4 x 5 + 5 y 3 By using the formula, ( a + b ) ( a – b ) = a 2 – b 2 We get, 4 x 5 - 5 y 3 4 x 5 + 5 y 3 = 4 x 5 2 - 5 y 3 2 = 16 25 x 2 - 25 9 y 2 . Thus, 4 x 5 - 5 y 3 4 x 5 + 5 y 3 = 16 25 x 2 - 25 9 y 2 .

Find the product of x + 1 x x - 1 x .

Given, x + 1 x x - 1 x By using the algebraic identity, ( a + b ) ( a – b ) = a 2 – b 2 , we have x + 1 x x - 1 x = x 2 - 1 x 2 = x 2 - 1 x 2 Thus, x + 1 x x - 1 x = x 2 - 1 x 2 .

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Mathematics Class 8>Chapter 6 - Operations on Algebraic Expressions>EXERCISE

R S Aggarwal Solutions for Chapter: Operations on Algebraic Expressions, Exercise 4: EXERCISE

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Chapter: Operations on Algebraic Expressions, Exercise 4: EXERCISE

Attempt the practice questions on Chapter 6: Operations on Algebraic Expressions, Exercise 4: EXERCISE with hints and solutions to strengthen your understanding. Mathematics Class 8 solutions are prepared by Experienced Embibe Experts.