Solve {l}{x^3-8y^3-6}{x^2y+12xy}

$$\left. \begin{array} { l } { x ^ { 3 } - 8 y ^ { 3 } - 6 } \\ { x ^ { 2 } y + 12 x y } \end{array} \right.$$

Least Common Multiple

$$-xy\left(x+12\right)\left(x^{3}-8y^{3}-6\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$12yx+yx^{2}=xy\left(x+12\right)$$

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

$$-xy\left(x+12\right)\left(x^{3}-8y^{3}-6\right)$$

Expand the expression.

$$8x^{2}y^{4}+96xy^{4}+72xy-yx^{5}-12yx^{4}+6yx^{2}$$

Evaluate

$$x^{3}-8y^{3}-6,\ xy\left(x+12\right)$$