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

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

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