Question

How do you factor `ab^2-ab-72a`?

Answer 1

Separate out the common factor `a`, then find a pair of factors of `72` that differ by `1` to find:

`ab^2-ab-72a = a(b-9)(b+8)`

Explanation:

First notice that all the terms are multiple of `a`, so we can separate `a` out as a factor to get:

`ab^2-ab-72a = a(b^2-b-72)`

Turning our attention to `b^2-b-72`, we need to find a pair of numbers whose product is `72` and whose difference is `1` (the coefficient of the middle term).

There are several quick ways to find the pair `9 xx 8 = 72`.

One way is to notice that `72` lies between the perfect squares `64 = 8^2` and `81 = 9^2`.

Anyway, we can deduce that `b^2-b-72 = (b-9)(b+8)`, giving us:

`ab^2-ab-72a = a(b-9)(b+8)`