Solve {l}{(3a-2b)^2-(2b-c)^2}{(2m-3n)^2}

$$\left. \begin{array} { l } { ( 3 a - 2 b ) ^ { 2 } - ( 2 b - c ) ^ { 2 } } \\ { ( 2 m - 3 n ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$-\left(3a-c\right)\left(c+3a-4b\right)\left(2m-3n\right)^{2}$$

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.

$$-\left(3a-c\right)\left(c+3a-4b\right)\left(2m-3n\right)^{2}$$

Expand the expression.

$$48abm^{2}+4c^{2}m^{2}-16bcm^{2}-36a^{2}m^{2}+48bcmn+108mna^{2}-144abmn-12mnc^{2}+108abn^{2}+9c^{2}n^{2}-36bcn^{2}-81a^{2}n^{2}$$

Evaluate

$$\left(3a-c\right)\left(c+3a-4b\right),\ \left(2m-3n\right)^{2}$$