Question

Factorise:
$x^4-(x-z{)}^4$

Answer 1

$x^4-(x-z{)}^4=(x^2{)}^2-\left(\right(x-z{)}^2{)}^2$

$=(x^2-(x-z{)}^2\left)\right(x^2+(x-z{)}^2)$

$=(x-(x-z\left)\right)(x+(x-z\left)\right)(x^2+(x-z{)}^2)$

$=(x-x+z)(x+x-z)(x^2+(x-z{)}^2)$

$=z(2x-z)(x^2+(x-z{)}^2)$

Hence factorised

Formula:

$a^2-b^2=(a-b)(a+b)$