# How do you multiply (x+3)(x-3)+(x+7)(x-3)?

Feb 13, 2016

$\textcolor{b l u e}{2 {x}^{2} + 4 x - 30}$

#### Explanation:

We can use the FOIL Method,
(First, Outer, Inner, and Last)

like this,

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

Solving the problem,

$\left(x + 3\right) \left(x - 3\right) + \left(x + 7\right) \left(x - 3\right)$

we can simplify the 1st term, $\left(x + 3\right) \left(x - 3\right)$

$\left(x + 3\right) \left(x - 3\right) = {x}^{2} - 3 x + 3 x - 9$

${x}^{2} - 3 x + 3 x - 9$, combine all like terms, to simplify, if there is any, like $- 3 x$ and $+ 3 x$, we can combine this.

Since $a + \left(- a\right) = 0$ (Additive Inverse Property), we can cancel the like terms giving,

$= {x}^{2} - 9$

now apply FOIL method, to the 2nd term.

$\left(x + 7\right) \left(x - 3\right) = {x}^{2} - 3 x + 7 x - 21$

simplify, by combining like terms,

$= {x}^{2} + 4 x - 21$

Plug it all,

${x}^{2} - 9 + {x}^{2} + 4 x - 21$

combine like terms to simplify again, we must simplify the answer as long as possible.

$= 2 {x}^{2} + 4 x - 30$