Question

x is to power of 4 - (x-z)is to power of 4

Answer 1

Answer:

The answer is $z(2x-z)(2x^2-2zx+z^2)$

Step-by-step explanation:

  $x^4-(x-z)^4$

$=(x^2)^2-[(x-z)^2]^2$, write in the form of $a^2-b^2$

$=(x^2-(x-z)^2)(x^2+(x-z)^2)$, since $a^2-b^2=(a-b)(a+b)$

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

( using above property and $(a-b)^2=a^2-2ab+b^2$ )

$=(x-x+z)(x+x-z)(2x^2-2zx+z^2)\\=z(2x-z)(2x^2-2zx+z^2)$