How do you combine like terms in #(7x ^ { 2} + x y - 3y ^ { 2} ) - ( - 4x ^ { 2} + 7x y + 12)#?

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Answer 1 · 2017-04-12T06:12:33

#11x^2-6xy-3y^2-12#

We have #(7x^2+xy-3y^2)-(-4x^2+7xy+12)#

This looks pretty nasty, but if we keep things organized and move one step at a time, we should be fine :)

First things first, let's distribute the negative into the second group:

#(7x^2+xy-3y^2)color(purple)(-)*-4x^2+color(purpel)(-)*7xy+color(purple)(-)*12#
#7x^2+xy-3y^2+4x^2-7xy-12#

Now that we don't have those pesky parentheses anymore, let's start simplifying.

I'll start with #x^2#
#color(blue)(7x^2)+xy-3y^2color(blue)(+4x^2)-7xy-12#
#(7x^2+4x^2)# is #11x^2#

That gives us #11x^2+xy-3y^2-7x^2-12#

I'm going to combine #xy# now:
#11x^2+color(red)(xy)-3y^2color(red)(-7xy)-12#
#(xy-7xy)# is #-6xy#

Now we have
#11x^2-6xy-3y^2-12#

There are no more like-terms, so we're done.