# How do you factor 6r^3m^3-42r^2m^2+54rm-378?

Jul 8, 2015

Factor out the GCF $6$. Then factor by grouping.

#### Explanation:

$6 {r}^{3} {m}^{3} - 42 {r}^{2} {m}^{2} + 54 r m - 378$

Factor out the GCF $6$.

$6 \left({r}^{3} {m}^{3} - 7 {r}^{2} {m}^{2} + 9 r m - 63\right)$

Factor by grouping.

$6 \left({r}^{3} {m}^{3} - 7 {r}^{2} {m}^{2}\right) + \left(9 r m - 63\right)$

Factor out common terms for both groups.

$6 \left({r}^{2} {m}^{2} \left(r m - 7\right)\right) + \left(9 \left(r m - 7\right)\right)$

Factor out the common term $\left(r m - 7\right)$.

$6 \left({r}^{2} {m}^{2} + 9\right) \left(r m - 7\right)$