Answer
$x^{4}-4x^{3}+6x^{2}-4x+1$
Work Step by Step
$(x-1)^{4} =( (x-1)^{2}) ^{2}$
Using the formula $(a-b)^{2}= a^{2}-2ab+b^{2}$
$ (x-1)^{2} = (x^{2}-2x+1)$
$=(x^{2}-2x+1)^{2}$
$=(x^{2}-2x+1)(x^{2}-2x+1)$
$=x^{4}-2x^{3}+x^{2}-2x^{3}+4x^{2}-2x+x^{2}-2x+1$
Combine like terms.
$=x^{4}-2x^{3}-2x^{3}+x^{2}+4x^{2}+x^{2}-2x-2x+1$
$=x^{4}-4x^{3}+6x^{2}-4x+1$
