Solve {l}{(a-b)}{(a^2-ab+b)^2}

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

Least Common Multiple

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

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.

$$\left(a-b\right)\left(-a^{4}-a^{2}b^{2}+2ab^{2}-b^{2}+2ba^{3}-2ba^{2}\right)$$

Expand the expression.

$$-a^{5}+a^{2}b^{3}+4a^{2}b^{2}-2ab^{3}-ab^{2}+b^{3}-3b^{2}a^{3}+3ba^{4}-2ba^{3}$$

Evaluate

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