Question

How do you factor the expression `9a^2b^3 -15ab^2+ 12a^3b^2`?

Answer 1

`9a^2b^3-15ab^2+12a^3b^2 = 3ab^2(3ab-5+4a^2)`

Explanation:

Given:

`9a^2b^3-15ab^2+12a^3b^2`

Note that all of the terms are divisible by `3`, `a` and `b^2`, hence by `3ab^2`.

So we can separate that out as a factor:

`9a^2b^3-15ab^2+12a^3b^2 = 3ab^2(3ab-5+4a^2)`

The remaining quadratic factor does not reduce any further, due to its mixture of terms in `a` and `b`.