Solve {l}{4x^{2}y^{4}-9z^{6}}{4x^{2}y^4-12xy^2z^3+9z^6}

$$\left. \begin{array} { l } { 4 x ^ { 2 } y ^ { 4 } - 9 z ^ { 6 } } \\ { 4 x ^ { 2 } y ^ { 4 } - 12 x y ^ { 2 } z ^ { 3 } + 9 z ^ { 6 } } \end{array} \right.$$

Least Common Multiple

$$\left(2xy^{2}+3z^{3}\right)\left(2xy^{2}-3z^{3}\right)^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$4x^{2}y^{4}-9z^{6}=\left(2xy^{2}-3z^{3}\right)\left(2xy^{2}+3z^{3}\right)$$

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

$$\left(2xy^{2}+3z^{3}\right)\left(2xy^{2}-3z^{3}\right)^{2}$$

Expand the expression.

$$8x^{3}y^{6}-12x^{2}z^{3}y^{4}-18xy^{2}z^{6}+27z^{9}$$

Evaluate

$$4x^{2}y^{4}-9z^{6},\ \left(2xy^{2}-3z^{3}\right)^{2}$$