Question

factorize completely. x^4 - (y + z)^4​

Answer 1

x4-(x-z)4 is the given expression

let (x-z) = y

So, x^4 - y^4 = (x^2)^2 - (y^2)^2 = {(x^2) + (y^2)} {(x^2) - (y^2)} = {(x^2) + (y^2)} (x+y) (x-y)

Put the value of y into the found expression

= {(x^2) + (y^2)} (x+y) (x-y)

= {x^2+(x-z)^2} (x+x-z) (x-x+z)

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

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