# How do you multiply (5k-5)(k^2-4k-5)?

Jun 30, 2017

See a 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.

$\left(\textcolor{red}{5 k} - \textcolor{red}{5}\right) \left(\textcolor{b l u e}{{k}^{2}} - \textcolor{b l u e}{4 k} - \textcolor{b l u e}{5}\right)$ becomes:

$\left(\textcolor{red}{5 k} \times \textcolor{b l u e}{{k}^{2}}\right) - \left(\textcolor{red}{5 k} \times \textcolor{b l u e}{4 k}\right) - \left(\textcolor{red}{5 k} \times \textcolor{b l u e}{5}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{{k}^{2}}\right) + \left(\textcolor{red}{5} \times \textcolor{b l u e}{4 k}\right) + \left(\textcolor{red}{5} \times \textcolor{b l u e}{5}\right)$

$5 {k}^{3} - 20 {k}^{2} - 25 k - 5 {k}^{2} + 20 k + 25$

We can now group and combine like terms:

$5 {k}^{3} - 20 {k}^{2} - 5 {k}^{2} - 25 k + 20 k + 25$

$5 {k}^{3} + \left(- 20 - 5\right) {k}^{2} + \left(- 25 + 20\right) k + 25$

$5 {k}^{3} + \left(- 25\right) {k}^{2} + \left(- 5\right) k + 25$

$5 {k}^{3} - 25 {k}^{2} - 5 k + 25$

Jun 30, 2017

color(green)(5k^3-25k^2-5k+25

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$${k}^{2} - 4 k - 5$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{5 k - 5}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$5 {k}^{3} - 20 {k}^{2} - 25 k$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$- 5 {k}^{2} + 20 k + 25$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{5 {k}^{3} - 25 {k}^{2} - 5 k + 25}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$color(green)(5k^3-25k^2-5k+25