Solve (2/3x^{2}-1/2xy+3/2y^{2})-5/2y^{2}|frac{2}{3}x^{3}-frac{1}{10}x^2y-frac{2}{3}xy^2|-frac{1}{3}xy(frac{2}{3}x^3-5y^3)

$$( \frac { 2 } { 3 } x ^ { 2 } - \frac { 1 } { 2 } x y + \frac { 3 } { 2 } y ^ { 2 } ) - \frac { 5 } { 2 } y ^ { 2 } | \frac { 2 } { 3 } x ^ { 3 } - \frac { 1 } { 10 } x ^ { 2 } y - \frac { 2 } { 3 } x y ^ { 2 } | - \frac { 1 } { 3 } x y ( \frac { 2 } { 3 } x ^ { 3 } - 5 y ^ { 3 } )$$

Factor

$$\frac{-45y^{2}|-\frac{yx^{2}}{10}-\frac{2xy^{2}}{3}+\frac{2x^{3}}{3}|+30xy^{4}-4yx^{4}-9xy+12x^{2}+27y^{2}}{18}$$

Solution Steps

Factor out \frac{1}{18}.

$$\frac{12x^{2}-9xy+27y^{2}-45y^{2}|\frac{2x^{3}}{3}-\frac{x^{2}y}{10}-\frac{2xy^{2}}{3}|-2xy\left(2x^{3}-15y^{3}\right)}{18}$$

Evaluate

$$-\frac{5y^{2}|-\frac{yx^{2}}{10}-\frac{2xy^{2}}{3}+\frac{2x^{3}}{3}|}{2}+\frac{5xy^{4}}{3}-\frac{2yx^{4}}{9}-\frac{xy}{2}+\frac{2x^{2}}{3}+\frac{3y^{2}}{2}$$