Question #32c33

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Answer 1 · 2014-08-14T19:00:33

The answer is #-(x+2)(x+12)#.

There are 2 ways to solve this problem. The first is to expand then factor.

#(2x+4)(x+3)-(3x+6)(x+6)#

FOIL first and second expressions:

#=(2x^2+10x+12)-(3x^2+24x+36)#

Simplify:

#=-x^2-14x-24#

Factor:

#=-(x+2)(x+12)#

The second way is to notice the common factors in the first and second expressions; factor:

#=2(x+2)(x+3)-3(x+2)(x+6)#

Use the distributive property:

#=(x+2)[2(x+3)-3(x+6)]#

Expand the second factor:

#=(x-2)[2x+6-3x-18]#

Simplify:

#=(x-2)(-x-12)#

Choose whichever way you are most comfortable with. The first way will always work, and the second way only applies for certain questions.