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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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