Solve {l}{m^3n+2m^2n^3}{2n(m-1)-m(m-1)}

$$\left. \begin{array} { l } { m ^ { 3 } n + 2 m ^ { 2 } n ^ { 3 } } \\ { 2 n ( m - 1 ) - m ( m - 1 ) } \end{array} \right.$$

Least Common Multiple

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

Solution Steps

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

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

Expand the expression.

$$4m^{3}n^{4}+2m^{3}n^{3}-4m^{2}n^{4}-2n^{3}m^{4}+2n^{2}m^{4}-2n^{2}m^{3}-nm^{5}+nm^{4}$$

Evaluate

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