# How do you foil (x-8)(x+4)?

Aug 6, 2015

${x}^{2} - 4 x - 32$

#### Explanation:

In FOIL, the "F" stands for "First" (times First), the "O" stands for "Outside" (times Outside), the "I" stands for "Inside" (times Inside), and the "L" stands for "Last" (times Last).

With the product $\left(x - 8\right) \left(x + 4\right)$ of the two binomials $x - 8$ and $x + 4$, First-times-First gives $x \cdot x = {x}^{2}$, Outside-times-Outside gives $x \cdot 4 = 4 x$, Inside-times-Inside is $- 8 \cdot x = - 8 x$, and Last-times-Last is $- 8 \cdot 4 = - 32$.

Hence, $\left(x - 8\right) \left(x + 4\right) = {x}^{2} + 4 x - 8 x - 32 = {x}^{2} - 4 x - 32$

The reasons the FOIL method works has to do with the distributive and commutative properties:

$\left(a + b\right) \cdot \left(c + d\right) = \left(a + b\right) \cdot c + \left(a + b\right) \cdot d$

$= a \cdot c + b \cdot c + a \cdot d + b \cdot d = a c + a d + b c + b d$