Question

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

Answer 1

`b^3(a^3b^3 - b^3)`

Explanation:

`a^3b^6 - b^3`

`b^6 = b^3 cdot b^3`

`(a^3b^3b^3 - b^3)`

factorizing;

`b^3(a^3b^3 - b^3)`

Answer 2

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

Explanation:

We want to simplify `a^3b^6-b^3`. The first thing to do is to factor out `b^3` to give `b^3(a^3b^3-1)`.

If we look carefully, we can see that `b^3(a^3b^3-1)=b^3((ab)^3-1^3)`. So now we can use a formula to simplify even more:

`a^3-b^3=(a-b)(a^2+ab+b^3)`

So

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