Solve {l}{(a^{2}bc)^2divab^2c}{(3mn+1)(3mn-1)-8m^2n^2}

$$\left. \begin{array} { l } { ( a ^ { 2 } b c ) ^ { 2 } \div a b ^ { 2 } c } \\ { ( 3 m n + 1 ) ( 3 m n - 1 ) - 8 m ^ { 2 } n ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$b^{4}\left(\left(mn\right)^{2}-1\right)\left(ac\right)^{3}$$

Solution Steps

Factor the expressions that are not already factored.

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

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

$$a^{3}c^{3}\left(mn-1\right)\left(mn+1\right)b^{4}$$

Expand the expression.

$$m^{2}n^{2}a^{3}c^{3}b^{4}-a^{3}c^{3}b^{4}$$

Evaluate

$$b^{4}\left(ac\right)^{3},\ \left(mn\right)^{2}-1$$