# How do you simplify 15a^3b^2 - 10 a^2b^2 + 14a^3b^2 - 5a^2b^2?

Mar 22, 2018

#### Answer:

${a}^{2} {b}^{2} \left(29 a - 15\right) = {\left(a b\right)}^{2} \left(29 a - 15\right)$

#### Explanation:

We need the greatest common factors in each term.

First we simplify to get: $29 {a}^{3} {b}^{2} - 15 {a}^{2} {b}^{2}$

There are no integers which divide into $29$ and $15$.

${a}^{2}$ goes into ${a}^{3}$ and ${a}^{2}$

All terms have ${b}^{2}$

So we factor out ${a}^{2} {b}^{2}$

${a}^{2} {b}^{2} \left(29 a - 15\right)$

If you want, we can factor ${a}^{2} {b}^{2} = {\left(a b\right)}^{2}$