Question

How do you factor `a^3*b^6 - b^3`?

Answer 1

`a^3*b^6-b^3=b^3*(a*b-1)(1+a*b+a^2*b^2)`

Explanation:

First, `a^3*b^6-b^3=(a^3*b^3-1)*b^3`.
Now there is a polynomial identity that can help us and which is
`(x^{n+1}-1)/(x-1)=1+x+x^2+x^3+...+x^n`
then
`a^3*b^3-1=(a*b-1)(1+a*b+a^2*b^2)`. Finally
`a^3*b^6-b^3=b^3*(a*b-1)(1+a*b+a^2*b^2)`