Factorize $x^4-( x-z)^4$.

Given: $x^4-( x-z)^4$.

To do: To factorize $x^4-( x-z)^4$.

Solution:

As given $x^4-( x-z)^4$

$x^4-( x-z)4$

$=( x^2)^2-[( x-z)^2]^2$

$=[x^2-(x-z)^2] [x^2+(x-z)^2]$

$=[x-(x-z)][x+(x-z)][x^2+x^2-2xz+z^2]$

$=z(2x-z)(2x^2-2xz+z^2)$

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Updated on: 10-Oct-2022

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