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

1 Answer

Answer:

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)#