We have the given expression as: x 8 - 1 We can also write this as: = x 4 2 - 1 2 Using identity: a 2 - b 2 = ( a - b ) ( a + b ) = x 4 + 1 x 4 - 1 Again, Using identity: a 2 - b 2 = ( a - b ) ( a + b ) x 8 - 1 = x 4 + 1 x 2 + 1 x + 1 x - 1 We can write x 4 + 1 = x 2 2 + 1 2 + 2 x 2 - 2 x 2 x 4 + 1 = x 2 + 1 2 - 2 x 2 Using the identity a 2 - b 2 = ( a - b ) ( a + b ) x 4 + 1 = ( x 2 + √ 2 x + 1 ) ( x 2 - √ 2 x + 1 ) Hence, x 8 - 1 = x 2 + √ 2 x + 1 x 2 - √ 2 x + 1 x 2 + 1 x + 1 x - 1 .

Secondary School Mathematics FOR CLASS 9>Algebra>Chapter 3 - Factorisation of Polynomials>EXERCISE 3B

R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: EXERCISE 3B

Author:R S Aggarwal & Veena Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: EXERCISE 3B

Attempt the free practice questions from Exercise 2: EXERCISE 3B with hints and solutions to strengthen your understanding. Secondary School Mathematics FOR CLASS 9 solutions are prepared by Experienced Embibe Experts.