Solve 15m^{5}-9m^{3}n^{2}-5m^{4}n+3m^2n^3+3mn^4-n^5)/(3m-n)

$$15 m ^ { 5 } - 9 m ^ { 3 } n ^ { 2 } - 5 m ^ { 4 } n + 3 m ^ { 2 } n ^ { 3 } + 3 m n ^ { 4 } - n ^ { 5 } ) / ( 3 m - n )$$

Factor

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

Solution Steps

Do the grouping 15m^{5}-9m^{3}n^{2}-5m^{4}n+3m^{2}n^{3}+3mn^{4}-n^{5}=\left(15m^{5}-9m^{3}n^{2}+3mn^{4}\right)+\left(-5m^{4}n+3m^{2}n^{3}-n^{5}\right), and factor out 3m in the first and -n in the second group.

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

Factor out common term 5m^{4}-3m^{2}n^{2}+n^{4} by using distributive property.

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

Evaluate

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