Solve x^3+2x,x^3+8

$$x ^ { 3 } + 2 x , x ^ { 3 } + 8$$

Least Common Multiple

$$x\left(x^{2}+2\right)\left(x^{3}+8\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{3}+2x=x\left(x^{2}+2\right) x^{3}+8=\left(x+2\right)\left(x^{2}-2x+4\right)$$

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

$$x\left(x+2\right)\left(x^{2}+2\right)\left(x^{2}-2x+4\right)$$

Expand the expression.

$$x^{6}+2x^{4}+8x^{3}+16x$$

Evaluate

$$x\left(x^{2}+2\right),x^{3}+8$$