Solve {l}{x^3+27}{(x^2-2x)}

$$\left. \begin{array} { l } { x ^ { 3 } + 27 } \\ { ( x ^ { 2 } - 2 x ) } \end{array} \right.$$

Least Common Multiple

$$x\left(x-2\right)\left(x^{3}+27\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{3}+27=\left(x+3\right)\left(x^{2}-3x+9\right) -2x+x^{2}=x\left(x-2\right)$$

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

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

Expand the expression.

$$x^{5}-2x^{4}+27x^{2}-54x$$

Evaluate

$$x^{3}+27,\ x\left(x-2\right)$$