Question

Factorise: a8 - b8


please solve this​

Answer 1

Answer:

(a - b)(a + b)(a² + b²)($a^{4}$ + $b^{4}$ )

Step-by-step 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 )($a^{4}$ + $b^{4}$ )