# How do you use FOIL to multiply (x+2)^3?

Jun 6, 2015

FOIL will only get you part of the way,

First + Outside + Inside + Last ...

$\left(x + 2\right) \left(x + 2\right) = \left(x \cdot x\right) + \left(x \cdot 2\right) + \left(2 \cdot x\right) + \left(2 \cdot 2\right)$

$= {x}^{2} + 2 x + 2 x + 4$

$= {x}^{2} + 4 x + 4$

Then

$\left({x}^{2} + 4 x + 4\right) \left(x + 2\right)$

$= \left({x}^{2} + 4 x + 4\right) \cdot x + \left({x}^{2} + 4 x + 4\right) \cdot 2$

$= {x}^{3} + 4 {x}^{2} + 4 x + 2 {x}^{2} + 8 x + 8$

$= {x}^{2} + 6 {x}^{2} + 12 x + 8$