Answer
$-x^{4}+x^{2}-2x+1$
Work Step by Step
Use the rule
$(A+B)(A-B)=A^{2}-B^{2}$:
with $A=x-1$ and $B=x^2$:
$(x-1+x^2)(x-1-x^2)=(x-1)^{2}-x^{4}$
Use the rule
$(A-B)^{2} = A^{2} - 2AB + B^{2}$
with $A=x$ and $B=1$ to expand the binomial in $(x-1)^{2}-x^{4}$:
$(x-1)^{2}-x^{4}=(x^{2} - 2(x)(1) + 1) - x^{4}$
$= x^{2} - 2x + 1 - x^{4}$
Rearrange:
$-x^{4}+x^{2}-2x+1$
