# How do you multiply polynomials (a + 3)(a - 2)?

Mar 27, 2018

${a}^{2} + a - 6$

#### Explanation:

$a \cdot a = {a}^{2}$

$a \cdot - 2 = - 2 a$

$3 \cdot a = 3 a$

$3 \cdot - 2 = - 6$

Now when we combine them all together we get:

${a}^{2} - 2 a + 3 a - 6$

We still need to simplify this since $- 2 a$ and $3 a$ are like terms. So the final answer is:
${a}^{2} + a - 6$

Hope this helps!

Mar 27, 2018

${a}^{2} + a - 6$

#### Explanation:

$\text{each term in the second factor is multiplied by each}$
$\text{term in the first factor}$

$\Rightarrow \left(\textcolor{red}{a + 3}\right) \left(a - 2\right)$

$= \textcolor{red}{a} \left(a - 2\right) \textcolor{red}{+ 3} \left(a - 2\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$= \left(\textcolor{red}{a} \times a\right) + \left(\textcolor{red}{a} \times - 2\right) + \left(\textcolor{red}{3} \times a\right) + \left(\textcolor{red}{3} \times - 2\right)$

$= {a}^{2} \textcolor{b l u e}{- 2 a} \textcolor{b l u e}{+ 3 a} - 6 \leftarrow \textcolor{b l u e}{\text{collect like terms}}$

$= {a}^{2} \textcolor{b l u e}{+ a} - 6$

$\Rightarrow \left(a + 3\right) \left(a - 2\right) = {a}^{2} + a - 6$