Question

factorise ...... x^4-(x-z)^4

Answer 1

x^4-(x-z)^4 can be factorised as,

=x^4-(x-z)^4

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

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

we used the following formula,

a^2-b^2=(a-b)(a+b)

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

we used  the following formula,

a^2-b^2=(a-b)(a+b)

(a-b)^2=a^2+b^2-2ab

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

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

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