# Question #32c33

Aug 14, 2014

The answer is $- \left(x + 2\right) \left(x + 12\right)$.

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

$\left(2 x + 4\right) \left(x + 3\right) - \left(3 x + 6\right) \left(x + 6\right)$

FOIL first and second expressions:

$= \left(2 {x}^{2} + 10 x + 12\right) - \left(3 {x}^{2} + 24 x + 36\right)$

Simplify:

$= - {x}^{2} - 14 x - 24$

Factor:

$= - \left(x + 2\right) \left(x + 12\right)$

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

$= 2 \left(x + 2\right) \left(x + 3\right) - 3 \left(x + 2\right) \left(x + 6\right)$

Use the distributive property:

$= \left(x + 2\right) \left[2 \left(x + 3\right) - 3 \left(x + 6\right)\right]$

Expand the second factor:

$= \left(x - 2\right) \left[2 x + 6 - 3 x - 18\right]$

Simplify:

$= \left(x - 2\right) \left(- x - 12\right)$

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