How do you add #(7x ^ { 3} - 5x ^ { 2} + 9x + 3) + ( 5x ^ { 3} - 7x ^ { 2} - x + 3)#?

1 Answer
Shantelle
Dec 18, 2017

#12x^3 - 12x^2 + 8 + 6#

Explanation:

#(7x^3 - 5x^2 + 9x + 3) + (5x^3 - 7x^2 - x + 3)#

This is the same as #7x^3 - 5x^2 + 9x + 3 + 5x^3 - 7x^2 - x + 3#.

The first thing we do is look for "like terms" and variables with the same degree. Our only variable here is #x#. We have #x^3#, #x^2#, #x#, and numbers.

Let's first combine the #x^3# values. We have #7x^3# and #5x^3#.
#7x^3 + 5x^3 = 12x^3#

Now #x^2#:
#-5x^2 - 7x^2 = -12x^2#

#x#:
#9x - x = 8x#

Numbers:
#3 + 3 = 6#

Now that we have simplified/combined each of the terms, let's put them together:
#12x^3 - 12x^2 + 8x + 6#

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