# How do you multiply -mnp(3m - 5n + 7p)?

Feb 28, 2016

$- 3 {m}^{2} n p + 5 m {n}^{2} p - 35 m n {p}^{2}$

#### Explanation:

$1$. Recall the distributive property: $a \left(b + c\right) = a b + a c$. Thus, in your equation, multiply $\textcolor{red}{- m n p}$ by each term inside the brackets.

$\textcolor{red}{- m n p} \left(3 m - 5 n + 7 p\right)$

$= \textcolor{red}{- \left(m n p\right)} \left(3 m\right) \textcolor{red}{- \left(m n p\right)} \left(- 5 n\right) \textcolor{red}{- \left(m n p\right)} \left(7 p\right)$

$2$. Simplify.

$= - 3 {m}^{2} n p + 5 m {n}^{2} p - 35 m n {p}^{2}$