Solve ax(m-n)^3,x^3(m^3-n^3)

$$a x ( m - n ) ^ { 3 } , x ^ { 3 } ( m ^ { 3 } - n ^ { 3 } )$$

Least Common Multiple

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

Solution Steps

Factor the expressions that are not already factored.

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

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

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

Expand the expression.

$$am^{2}n^{3}x^{3}+ax^{3}n^{5}+2anx^{3}m^{4}-an^{2}m^{3}x^{3}-2amx^{3}n^{4}-ax^{3}m^{5}$$

Evaluate

$$ax\left(m-n\right)^{3},\left(mx\right)^{3}-\left(nx\right)^{3}$$