# How do you find the product (k-m)(k+m)(k-m)?

May 2, 2017

See the entire solution process below:

#### Explanation:

First, we can multiply the two terms on the left of the expression using this rule and substituting $k$ for $a$ and $m$ for $b$:

$\left(a + b\right) \left(a - b\right) = {a}^{a} - {b}^{2}$

(color(red)((k - m))color(blue)((k + m))(k - m) => (k^2 - m^2)(k - m)

Next, we can multiply these two remaining terms by multiplying each term in the parenthesis on the left by each term in the parenthesis on the right:

$\textcolor{red}{\left({k}^{2} - {m}^{2}\right)} \textcolor{b l u e}{\left(k - m\right)} \implies$

$\left(\textcolor{red}{{k}^{2}} \cdot \textcolor{b l u e}{k}\right) - \left(\textcolor{red}{{k}^{2}} \cdot \textcolor{b l u e}{m}\right) - \left(\textcolor{red}{{m}^{2}} \cdot \textcolor{b l u e}{k}\right) + \left(\textcolor{red}{{m}^{2}} \cdot \textcolor{b l u e}{m}\right) \implies$

${k}^{3} - {k}^{2} m - k {m}^{2} + {m}^{3}$