Solve {l}{c^2-4cd-21d^2}{3m^2-16mn-12n^2}

$$\left. \begin{array} { l } { c ^ { 2 } - 4 c d - 21 d ^ { 2 } } \\ { 3 m ^ { 2 } - 16 m n - 12 n ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(c-7d\right)\left(m-6n\right)\left(c+3d\right)\left(3m+2n\right)$$

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.

$$\left(c-7d\right)\left(m-6n\right)\left(c+3d\right)\left(3m+2n\right)$$

Expand the expression.

$$3c^{2}m^{2}-12cdm^{2}-63d^{2}m^{2}+64cdmn+336mnd^{2}-16mnc^{2}+48cdn^{2}+252d^{2}n^{2}-12c^{2}n^{2}$$

Evaluate

$$\left(c-7d\right)\left(c+3d\right),\ \left(m-6n\right)\left(3m+2n\right)$$