Factorise: x^4– (x – z)^4 - Vidyadip

Question

Factorise: $x^4– (x – z)^4$

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Answer

$x^4-(x-z)^4$
$\left(x^2\right)^2-\left\{(x-z)^2\right\}^2. . . .$ [Using Identity $III$
$=\left\{x^2-(x-z)^2\right\}\left\{x^2+(x-z)^2\right\} . . . .$ [Applying Identity $III$
$=(x-x+z)(x+x-z)\left\{x^2+(x-z)^2\right\}$
$=z(2 x-z)\left\{x^2+(x-z)^2\right\}$
$=z(2 x-z)\left(x^2+x^2-2 x z+z^2\right). . . . $[Using Identity $II$
$=z(2 x-z)\left(2 x^2-2 x z+z^2\right)$

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