factorise

Question

Fully factorise in prime factors 1. (2x^16)-1/8

Answer 1

The expression is 2x16- 1/8.

= (1/8)[16x16- 1]

= (1/8)[(4x8)2-  12]

= (1/8)[4x8 +  1][4x8 - 1]

= (1/8)[4x8 +  1][(2x4)2- 12]

= (1/8) [4x8 +  1] [2x4 + 1] [2x4 - 1]

= (1/8) [4x8 +  1] [2x4 + 1] [(√2x2)2- 12]

= (1/8) [4x8 +  1] [2x4 + 1] [√2x2 + 1] [√2x2 - 1]

The factor form of 2x16- 1/8 = (1/8) [4x8 +  1] [2x4 + 1] [√2x2 + 1] [√2x2 - 1].