Solve 7m^7n-28mn^3

$$7 m ^ { 7 } n - 28 m n ^ { 3 }$$

Factor

$$7mn\left(m^{3}-2n\right)\left(m^{3}+2n\right)$$

Solution Steps

Factor out 7.

$$7\left(m^{7}n-4mn^{3}\right)$$

Consider m^{7}n-4mn^{3}. Factor out mn.

$$mn\left(m^{6}-4n^{2}\right)$$

Consider m^{6}-4n^{2}. Rewrite m^{6}-4n^{2} as \left(m^{3}\right)^{2}-\left(2n\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression.

$$7mn\left(m^{3}-2n\right)\left(m^{3}+2n\right)$$

Evaluate

$$7mn\left(m^{6}-4n^{2}\right)$$