Solve 10m^{2}n^{3}+15m^3n^2-5m^2n^3

$$10 m ^ { 2 } n ^ { 3 } + 15 m ^ { 3 } n ^ { 2 } - 5 m ^ { 2 } n ^ { 3 }$$

Factor

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

Solution Steps

Factor out 5.

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

Consider 2m^{2}n^{3}+3m^{3}n^{2}-m^{2}n^{3}. Factor out m^{2}n^{2}.

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

Consider 2n+3m-n. Multiply and combine like terms.

$$3m+n$$

Rewrite the complete factored expression.

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

Evaluate

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