Question

Factorise: a8 - b8


please solve this​

Answer 1

(a - b)(a + b)(a² + b²)(
`a^(4)` +
`b^(4)` )

Explanation:

by repeated use of the difference of squares factorising method, that is

a² - b² = (a - b)(a + b)

given

`a^(8)` -
`b^(8)`

= (
`a^(4)` )² - (
`b^(4)` )²

= (
`a^(4)` -
`b^(4)` )(
`a^(4)` +
`b^(4)` ) ← factor left parenthesis using difference of squares

= ( a² - b²)(a² + b²)(
`a^(4)` +
`b^(4)` ) ← factor left parenthesis by difference of squares

= (a - b)(a + b)(a² + b² )(
`a^(4)` +
`b^(4)` )