How do you multiply #(x + -1x^2)(x^2 + -1x)#?

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Answer 1 · 2018-07-07T13:41:22

#-x^4+2x^3-x^2#

Note that

#x+-x^2=x-x^2#
and

#x^2+-x=x^2-x#

So we get

(x-x^2)(x^2-x)=-(x^2-x)(x^2-x)=-(x^2-x)^2#

Using that #(a+b)^2=a^2+2ab+b^2#

we obtain

#-(x^4-2x^3+x^2)=-x^4+2x^3-x^2#