# How do you multiply (3n-2)(3n^2-8n-5)?

Dec 21, 2016

$9 {n}^{3} - 30 {n}^{2} + n + 10$

#### Explanation:

To multiply the two terms in this expression you must multiply each term within the left parenthesis by each term in the right parenthesis:

$\left(\textcolor{red}{3 n - 2}\right) \left(\textcolor{b l u e}{3 {n}^{2} - 8 n - 5}\right) \to$

$\left(\textcolor{red}{3 n} \cdot \textcolor{b l u e}{3 {n}^{2}}\right) - \left(\textcolor{red}{3 n} \cdot \textcolor{b l u e}{8 n}\right) - \left(\textcolor{red}{3 n} \cdot \textcolor{b l u e}{5}\right) - \left(\textcolor{red}{2} \cdot \textcolor{b l u e}{3 {n}^{2}}\right) + \left(\textcolor{red}{2} \cdot \textcolor{b l u e}{8 n}\right) + \left(\textcolor{red}{2} \cdot \textcolor{b l u e}{5}\right) \to$

$9 {n}^{3} - 24 {n}^{2} - 15 n - 6 {n}^{2} + 16 n + 10$

Now we can group and combine like terms:

$9 {n}^{3} - 24 {n}^{2} - 6 {n}^{2} - 15 n + 16 n + 10$

$9 {n}^{3} - \left(24 + 6\right) {n}^{2} + \left(- 15 + 16\right) n + 10$

$9 {n}^{3} - 30 {n}^{2} + 1 n + 10$

$9 {n}^{3} - 30 {n}^{2} + n + 10$