# How do you simplify 4x^2y + 8xy^2 - 9x^2y - 4xy^2 + 15 x^2y?

Combine like terms, then find what is common amongst what's left and you'll get to
$\left(2 x y\right) \left(5 x + 2 y\right)$

#### Explanation:

To simplify this expression, we look for the common terms and simplify them first:

$4 {x}^{2} y + 8 x {y}^{2} - 9 {x}^{2} y - 4 x {y}^{2} + 15 {x}^{2} y$

There are some terms that are ${x}^{2} y$ and some that are $x {y}^{2}$. So let's rewrite the original to have like terms next to each other:

$4 {x}^{2} y - 9 {x}^{2} y + 15 {x}^{2} y + 8 x {y}^{2} - 4 x {y}^{2}$

Now we can see that the ${x}^{2} y$ terms have coefficients of 4, -9, and 15. We can sum those up and get 10. We can also see that the $x {y}^{2}$ terms have coefficients of 8 and -4, which we can sum up and get 4. Let's have a look at what it looks like now:

$10 {x}^{2} y + 4 x {y}^{2}$

Now we can find common factors in these two terms and factor them out (I see 2xy):

$\left(2 x y\right) \left(5 x + 2 y\right)$