# How do you find the product -9g(-2g+g^2)+3(g^2+4)?

Jul 9, 2017

See a solution process below:

#### Explanation:

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

$\textcolor{red}{- 9 g} \left(- 2 g + {g}^{2}\right) + \textcolor{b l u e}{3} \left({g}^{2} + 4\right) \implies$

$\left(\textcolor{red}{- 9 g} \times - 2 g\right) + \left(\textcolor{red}{- 9 g} \times - {g}^{2}\right) + \left(\textcolor{b l u e}{3} \times {g}^{2}\right) + \left(\textcolor{b l u e}{3} \times 4\right) \implies$

$18 {g}^{2} + \left(- 9 {g}^{3}\right) + 3 {g}^{2} + 12 \implies$

$18 {g}^{2} - 9 {g}^{3} + 3 {g}^{2} + 12$

Next, group like terms:

$- 9 {g}^{3} + 18 {g}^{2} + 3 {g}^{2} + 12$

Now, combine like terms:

$- 9 {g}^{3} + \left(18 + 3\right) {g}^{2} + 12$

$- 9 {g}^{3} + 21 {g}^{2} + 12$