Solve 18m^3+6m^2n-18m-6n

$$18 m ^ { 3 } + 6 m ^ { 2 } n - 18 m - 6 n$$

Factor

$$6\left(m-1\right)\left(m+1\right)\left(3m+n\right)$$

Solution Steps

Factor out 6.

$$6\left(3m^{3}+m^{2}n-3m-n\right)$$

Consider 3m^{3}+m^{2}n-3m-n. Do the grouping 3m^{3}+m^{2}n-3m-n=\left(3m^{3}+m^{2}n\right)+\left(-3m-n\right), and factor out m^{2} in the first and -1 in the second group.

$$m^{2}\left(3m+n\right)-\left(3m+n\right)$$

Factor out common term 3m+n by using distributive property.

$$\left(3m+n\right)\left(m^{2}-1\right)$$

Consider m^{2}-1. Rewrite m^{2}-1 as m^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m-1\right)\left(m+1\right)$$

Rewrite the complete factored expression.

$$6\left(3m+n\right)\left(m-1\right)\left(m+1\right)$$

Evaluate

$$6\left(3m+n\right)\left(m^{2}-1\right)$$