Solve {l}{(3x^{4}y^{3}+2x^{5}y^{2})^{2}}{(x^{2}y+2x^{3}y^2)(x^2y-2x^3y^2)}

$$\left. \begin{array} { l } { ( 3 x ^ { 4 } y ^ { 3 } + 2 x ^ { 5 } y ^ { 2 } ) ^ { 2 } } \\ { ( x ^ { 2 } y + 2 x ^ { 3 } y ^ { 2 } ) ( x ^ { 2 } y - 2 x ^ { 3 } y ^ { 2 } ) } \end{array} \right.$$

Least Common Multiple

$$\left(2x+3y\right)^{2}y^{4}\left(4\left(xy\right)^{2}-1\right)x^{8}$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{4}y^{2}-4x^{6}y^{4}=y^{2}\left(-2xy-1\right)\left(2xy-1\right)x^{4}$$

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

$$\left(2x+3y\right)^{2}\left(2xy-1\right)\left(2xy+1\right)y^{4}x^{8}$$

Expand the expression.

$$36y^{8}x^{10}+48y^{7}x^{11}+16y^{6}x^{12}-9y^{6}x^{8}-12y^{5}x^{9}-4y^{4}x^{10}$$

Evaluate

$$\left(2x+3y\right)^{2}y^{4}x^{8},\ y^{2}x^{4}\left(1-4\left(xy\right)^{2}\right)$$