How do you combine #3x ^ { 2} ( 3x - 2) - 9x ( 3x - 2) ^ { 2}#?

1 Answer
Fir3hawk
May 19, 2017

Distribute, then combine like terms

Explanation:

First of all, group the equation into two separate parts:

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

The negative nine is isolated with the second grouping, as it needs to be distributed.

Now, for part one: #3x^2(3x-2)#
Distribute the #3x^2# to both terms in the parentheses

#3x^2(3x-2) = 9x^3 - 6x^2#

Make sure to multiply the coefficients, and remember that the exponent on the variable needs to be increased. When multiplying two variables together, remember to multiply the coefficients as well as add the powers together

Now, for part two: #-9(3x-2)^2#

At first glance, it looks like we do the same process for step 1. however, the term of #3x-2# is being squared, so before we distribute, we must FOIL this out

#(3x-2)^2 = (3x-2)(3x-2) = 9x^2-6x-6x+4#
# = 9x^2-12x+4#

Now, we have to distribute the -9 to each term in the equation

#-9(9x^2-12x+4) = -81x^2+108x-36#

For the last step, combine the two parts of the equation, combining like terms

#9x^3 - 6x^2+(-81x^2+108x-36) #
#= 9x^3 - 6x^2 - 81x^2 +108x -36#
#= 9x^3 - 87x^2 +108x -36#

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