# How do you multiply (3m+1)(m-4)(m+5)?

Nov 12, 2014

$\left(3 m + 1\right) \left(m - 4\right) \left(m + 5\right)$

by distributing $\left(m - 4\right)$ to $3 m$ and $1$,

$= \left[3 m \left(m - 4\right) + 1 \left(m - 4\right)\right] \left(m + 5\right)$

by distributing $3 m$,

$= \left(3 {m}^{2} - 12 m + m - 4\right) \left(m + 5\right)$

by collecting like terms,

$= \left(3 {m}^{2} - 11 m - 4\right) \left(m + 5\right)$

by distributing $\left(m + 5\right)$,

$= 3 {m}^{2} \left(m + 5\right) - 11 m \left(m + 5\right) - 4 \left(m + 5\right)$

by distributing $3 {m}^{2}$, $- 11 m$, and $- 4$,

$= 3 {m}^{3} + 15 {m}^{2} - 11 {m}^{2} - 55 m - 4 m - 20$

by collecting like terms,

$= 3 {m}^{3} + 4 {m}^{2} - 59 m - 20$

I hope that this was helpful.