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

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Solution

Now,
$x^{4} - (x - z)^{4}$

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

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

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

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

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