# How do you find the product a(-8a^2+2a+4)+3(6a^2-4)?

Aug 6, 2017

See a solution process below:

#### Explanation:

First, expand both the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{a} \left(- 8 {a}^{2} + 2 a + 4\right) + \textcolor{b l u e}{3} \left(6 {a}^{2} - 4\right) \implies$

$\left(\textcolor{red}{a} \times - 8 {a}^{2}\right) + \left(\textcolor{red}{a} \times 2 a\right) + \left(\textcolor{red}{a} \times 4\right) + \left(\textcolor{b l u e}{3} \times 6 {a}^{2}\right) - \left(\textcolor{b l u e}{3} \times 4\right) \implies$

$- 8 {a}^{3} + 2 {a}^{2} + 4 a + 18 {a}^{2} - 12$

Next, group like terms:

$- 8 {a}^{3} + 2 {a}^{2} + 18 {a}^{2} + 4 a - 12$

Now, combine like terms:

$- 8 {a}^{3} + \left(2 + 18\right) {a}^{2} + 4 a - 12$

$- 8 {a}^{3} + 20 {a}^{2} + 4 a - 12$