# How do you multiply (-3u+3)(u^3-1)?

Mar 30, 2017

See the entire solution process below:

#### Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{- 3 u} + \textcolor{red}{3}\right) \left(\textcolor{b l u e}{{u}^{3}} - \textcolor{b l u e}{1}\right)$ becomes:

$\left(\textcolor{red}{- 3 u} \times \textcolor{b l u e}{{u}^{3}}\right) + \left(\textcolor{red}{- 3 u} \times \textcolor{b l u e}{- 1}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{{u}^{3}}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{- 1}\right)$

$- 3 {u}^{4} + 3 u + 3 {u}^{3} - 3$

$- 3 {u}^{4} + 3 {u}^{3} + 3 u - 3$

Mar 30, 2017

$- 3 {u}^{4} + 3 {u}^{3} + 3 u - 3$

#### Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket. This is demonstrated below.

$\left(\textcolor{red}{- 3 u + 3}\right) \left({u}^{3} - 1\right)$

$= \textcolor{red}{- 3 u} \left({u}^{3} - 1\right) \textcolor{red}{+ 3} \left({u}^{3} - 1\right)$

distribute brackets and simplify.

$= - 3 {u}^{4} + 3 u + 3 {u}^{3} - 3$

$= - 3 {u}^{4} + 3 {u}^{3} + 3 u - 3 \leftarrow \textcolor{red}{\text{ in standard form}}$