Solve {l}{3mx-2ny-2nx+6m+3my-4n}{mn^{4}-5m^{2}n^3+4m^3n^2-2m^4n}

$$\left. \begin{array} { l } { 3 m x - 2 n y - 2 n x + 6 m + 3 m y - 4 n } \\ { m n ^ { 4 } - 5 m ^ { 2 } n ^ { 3 } + 4 m ^ { 3 } n ^ { 2 } - 2 m ^ { 4 } n } \end{array} \right.$$

Least Common Multiple

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

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.

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

Expand the expression.

$$23xm^{3}n^{3}+2mxn^{5}+6nxm^{5}-16xn^{2}m^{4}-13xm^{2}n^{4}+23ym^{3}n^{3}+2myn^{5}+6nym^{5}-16yn^{2}m^{4}-13ym^{2}n^{4}+46m^{3}n^{3}+4mn^{5}+12nm^{5}-32n^{2}m^{4}-26m^{2}n^{4}$$

Evaluate

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