Solve {l}{2x^{2}(x^2+xy-2y^2)}{(y^2-6)(y^2+4)}

$$\left. \begin{array} { l } { 2 x ^ { 2 } ( x ^ { 2 } + x y - 2 y ^ { 2 } ) } \\ { ( y ^ { 2 } - 6 ) ( y ^ { 2 } + 4 ) } \end{array} \right.$$

Least Common Multiple

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

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.

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

Expand the expression.

$$-2x^{4}y^{4}+48x^{4}-2x^{3}y^{5}+4x^{3}y^{3}+4x^{2}y^{6}-8x^{2}y^{4}-96x^{2}y^{2}+4y^{2}x^{4}+48yx^{3}$$

Evaluate

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