How do you factor completely $x^2(a^2+2ab+b^2) = x(a+b)$ ?

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Answer 1 · 2015-06-16T14:22:58

You can first factor $(a^2+2ab+b^2)=(a+b)^2$

The left part can then be rewritten:
$x^2*(a+b)^2=[x(a+b)]^2$
The complete equation changes into:
$[x(a+b)]^2=x(a+b)$

This is of the form $Q^2=Q$ and there are only two solutions:
$Q=0orQ=1$

For $Q=0->x=0or(a+b)=0->a=-b$

For $Q=1->x*(a+b)=1->x=1/(a+b)$

How do you factor completely x^2(a^2+2ab+b^2) = x(a+b)x^2(a^2+2ab+b^2) = x(a+b)?