Solve {l}{(x+3)(x-3)(x^2+9)}{(-8a+11b)^2}

$$\left. \begin{array} { l } { ( x + 3 ) ( x - 3 ) ( x ^ { 2 } + 9 ) } \\ { ( - 8 a + 11 b ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(8a-11b\right)^{2}\left(x^{4}-81\right)$$

Solution Steps

Factor the expressions that are not already factored.

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

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

$$\left(x-3\right)\left(x+3\right)\left(8a-11b\right)^{2}\left(x^{2}+9\right)$$

Expand the expression.

$$64a^{2}x^{4}+121b^{2}x^{4}-176abx^{4}+14256ab-9801b^{2}-5184a^{2}$$

Evaluate

$$x^{4}-81,\ \left(11b-8a\right)^{2}$$