Solve {l}{x^{2}y^3-xy^2}{a^2xy+aby^2}

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

Least Common Multiple

$$axy^{2}\left(xy-1\right)\left(ax+by\right)$$

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.

$$axy^{2}\left(xy-1\right)\left(ax+by\right)$$

Expand the expression.

$$a^{2}x^{3}y^{3}+abx^{2}y^{4}-a^{2}x^{2}y^{2}-abxy^{3}$$

Evaluate

$$xy^{2}\left(xy-1\right),\ ay\left(ax+by\right)$$