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

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

Least Common Multiple

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

Solution Steps

Factor the expressions that are not already factored.

$$-xby+6xy-3x=x\left(-by+6y-3\right) y^{3}-8=\left(y-2\right)\left(y^{2}+2y+4\right)$$

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

$$x\left(y-2\right)\left(y^{2}+2y+4\right)\left(by-6y+3\right)$$

Expand the expression.

$$bxy^{4}-6xy^{4}+3xy^{3}-8bxy+48xy-24x$$

Evaluate

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