Question

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

Answer 1

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

Explanation:

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)`