Solve {l}{x^{3}y^3(xy^6)}{5x^3-5xy^6}

$$\left. \begin{array} { l } { x ^ { 3 } y ^ { 3 } ( x y ^ { 6 } ) } \\ { 5 x ^ { 3 } - 5 x y ^ { 6 } } \end{array} \right.$$

Least Common Multiple

$$-5x^{4}\left(x^{2}-y^{6}\right)y^{9}$$

Solution Steps

Factor the expressions that are not already factored.

$$5x^{3}-5xy^{6}=5x\left(x-y^{3}\right)\left(x+y^{3}\right)$$

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

$$5\left(-x-y^{3}\right)\left(x-y^{3}\right)x^{4}y^{9}$$

Expand the expression.

$$-5x^{6}y^{9}+5x^{4}y^{15}$$

Evaluate

$$x^{4}y^{9},\ 5x\left(x^{2}-y^{6}\right)$$