Solve {l}{a^{3}+3a^{2}b-3ab^{2}+b^{3}}{a^3-3a^2b+3ab^2-b^3}

$$\left. \begin{array} { l } { a ^ { 3 } + 3 a ^ { 2 } b - 3 a b ^ { 2 } + b ^ { 3 } } \\ { a ^ { 3 } - 3 a ^ { 2 } b + 3 a b ^ { 2 } - b ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$\left(a-b\right)^{3}\left(-a^{3}+3ab^{2}-b^{3}-3ba^{2}\right)$$

Solution Steps

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

$$\left(a-b\right)^{3}\left(-a^{3}+3ab^{2}-b^{3}-3ba^{2}\right)$$

Expand the expression.

$$-a^{6}-18a^{3}b^{3}+15a^{2}b^{4}-6ab^{5}+b^{6}+9b^{2}a^{4}$$

Evaluate

$$a^{3}-3ab^{2}+b^{3}+3ba^{2},\ \left(a-b\right)^{3}$$