Question

How do you find the product `(n-p)^2(n+p)`?

Answer 1

`n^3-np^2-n^2p+p^3`

Explanation:

We can write `(n-p)^2` as `(n-p)(n-p)`:

`(n-p)^2(n+p)=(n-p)(n-p)(n+p)`

We can group `(n-p)` and `(n+p)` and multiply those, since they will result in a difference of squares, which is only two terms instead of three. That will make our future distribution easier.

`=(n-p){(n-p)(n+p)}=(n-p)(n^2-p^2)`

Now distribute:

`=n(n^2-p^2)-p(n^2-p^2)`

`=n^3-np^2-n^2p+p^3`