Solve {l}{(-3xy+2)^3}{(y-4)(y+4)}

$$\left. \begin{array} { l } { ( - 3 x y + 2 ) ^ { 3 } } \\ { ( y - 4 ) ( y + 4 ) } \end{array} \right.$$

Least Common Multiple

$$\left(y^{2}-16\right)\left(3xy-2\right)^{3}$$

Solution Steps

Factor the expressions that are not already factored.

$$y^{2}-16=\left(y-4\right)\left(y+4\right)$$

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

$$\left(y-4\right)\left(y+4\right)\left(3xy-2\right)^{3}$$

Expand the expression.

$$27x^{3}y^{5}-432x^{3}y^{3}-54x^{2}y^{4}+864x^{2}y^{2}+36xy^{3}-576xy-8y^{2}+128$$

Evaluate

$$\left(2-3xy\right)^{3},\ y^{2}-16$$