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

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Solution

$x^{4} - (x - Z)^{4}$
$= (x^{2})^{2} - [(x - 2)^{2}]^{2}$
$= (x^{2} - (x - 2)^{2}) (x^{2} + (x - 2)) (x^{2} + x^{2} + z^{2} - 2 x z)$
$z (2 x - z) (2 x^{2} + z^{2} - 2 x z)$ $
$∴ x^{4} - (x - z)^{4} = z (2 x - 2) (2 x^{2} + z^{2} - 2 x z)$

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