Solve {l}{(x+3)(x^2+9)(x-3)}{(8m+6n)(8m-6n)}

$$\left. \begin{array} { l } { ( x + 3 ) ( x ^ { 2 } + 9 ) ( x - 3 ) } \\ { ( 8 m + 6 n ) ( 8 m - 6 n ) } \end{array} \right.$$

Least Common Multiple

$$-4\left(16m^{2}-9n^{2}\right)\left(x^{4}-81\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{4}-81=\left(x-3\right)\left(x+3\right)\left(x^{2}+9\right) 64m^{2}-36n^{2}=4\left(4m-3n\right)\left(4m+3n\right)$$

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

$$4\left(x-3\right)\left(x+3\right)\left(4m-3n\right)\left(3n+4m\right)\left(-x^{2}-9\right)$$

Expand the expression.

$$36n^{2}x^{4}-64m^{2}x^{4}-2916n^{2}+5184m^{2}$$

Evaluate

$$x^{4}-81,\ 64m^{2}-36n^{2}$$