Solve {l}{a^3+27b^3}{x^3+125}

$$\left. \begin{array} { l } { a ^ { 3 } + 27 b ^ { 3 } } \\ { x ^ { 3 } + 125 } \end{array} \right.$$

Least Common Multiple

$$\left(x^{3}+125\right)\left(27b^{3}+a^{3}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$a^{3}+27b^{3}=\left(a+3b\right)\left(a^{2}-3ab+9b^{2}\right) x^{3}+125=\left(x+5\right)\left(x^{2}-5x+25\right)$$

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

$$\left(x+5\right)\left(a+3b\right)\left(x^{2}-5x+25\right)\left(a^{2}+9b^{2}-3ab\right)$$

Expand the expression.

$$a^{3}x^{3}+27b^{3}x^{3}+125a^{3}+3375b^{3}$$

Evaluate

$$27b^{3}+a^{3},\ x^{3}+125$$