Question

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

Answer 1

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

Explanation:

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

`4x^2y+8xy^2-9x^2y-4xy^2+15x^2y`

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

`4x^2y-9x^2y+15x^2y+8xy^2-4xy^2`

Now we can see that the `x^2y` terms have coefficients of 4, -9, and 15. We can sum those up and get 10. We can also see that the `xy^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:

`10x^2y+4xy^2`

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

`(2xy)(5x+2y)`