Difference of Squares (Factoring)

Question

I have no idea whatsoever how to factor out this:

$$ab^2 - a$$

I know how to solve $a^2 - 4$: $$(a-2)(a+2)$$ But in that case, how can I factor out the $- a$ part?

Answer 1

You can factor in two steps: $ab^2 - a = a(b^2 - 1)$ and then continue to factor $b^2 - 1$, which it seems you know how to do.

Answer 2

$$ab^2 - a = a(b^2 - 1) = a(b-1)(b+1)$$

Answer 3

In problem like these, always ask yourself this question "what do these terms have in common" once you can figure that out then take that common factor out. In this case $ab^2 - a$. both terms have $a$ in common so you take that has the common factor. $a(b^2-1)$ and now you know how to proceed about how to factor a binomial. basically $b^2=1$ then take square root of both side you have $b= 1$ or $-1$ so the final answer will be $a(b-1)(b+1)$. Hope that bring more clarity when come to factoring binomials.