Solve 1/5x^{2}y-(1/3x^{2}y^{3})+(-3/2x^{2}y^{3})-0,3x^{2}y+(-1/6x^{2}y^3)-(-frac{5}{6}x^2y)-frac{1}{2}x^2y^3

$$\frac { 1 } { 5 } x ^ { 2 } y - ( \frac { 1 } { 3 } x ^ { 2 } y ^ { 3 } ) + ( - \frac { 3 } { 2 } x ^ { 2 } y ^ { 3 } ) - 0,3 x ^ { 2 } y + ( - \frac { 1 } { 6 } x ^ { 2 } y ^ { 3 } ) - ( - \frac { 5 } { 6 } x ^ { 2 } y ) - \frac { 1 } { 2 } x ^ { 2 } y ^ { 3 }$$

Factor

$$\frac{yx^{2}\left(22-75y^{2}\right)}{30}$$

Solution Steps

The opposite of -\frac{5}{6}x^{2}y is \frac{5}{6}x^{2}y.

$$factor(\frac{1}{5}x^{2}y-\frac{1}{3}x^{2}y^{3}-\frac{3}{2}x^{2}y^{3}-0,3x^{2}y-\frac{1}{6}x^{2}y^{3}+\frac{5}{6}x^{2}y-\frac{1}{2}x^{2}y^{3})$$

Combine -\frac{1}{6}x^{2}y^{3} and -\frac{1}{2}x^{2}y^{3} to get -\frac{2}{3}x^{2}y^{3}.

$$factor(\frac{1}{5}x^{2}y-\frac{1}{3}x^{2}y^{3}-\frac{3}{2}x^{2}y^{3}-0,3x^{2}y-\frac{2}{3}x^{2}y^{3}+\frac{5}{6}x^{2}y)$$

Combine -\frac{1}{3}x^{2}y^{3} and -\frac{3}{2}x^{2}y^{3} to get -\frac{11}{6}x^{2}y^{3}.

$$factor(\frac{1}{5}x^{2}y-\frac{11}{6}x^{2}y^{3}-0,3x^{2}y-\frac{2}{3}x^{2}y^{3}+\frac{5}{6}x^{2}y)$$

Combine \frac{1}{5}x^{2}y and -0,3x^{2}y to get -\frac{1}{10}x^{2}y.

$$factor(-\frac{1}{10}x^{2}y-\frac{11}{6}x^{2}y^{3}-\frac{2}{3}x^{2}y^{3}+\frac{5}{6}x^{2}y)$$

Combine -\frac{11}{6}x^{2}y^{3} and -\frac{2}{3}x^{2}y^{3} to get -\frac{5}{2}x^{2}y^{3}.

$$factor(-\frac{1}{10}x^{2}y-\frac{5}{2}x^{2}y^{3}+\frac{5}{6}x^{2}y)$$

Combine -\frac{1}{10}x^{2}y and \frac{5}{6}x^{2}y to get \frac{11}{15}x^{2}y.

$$factor(\frac{11}{15}x^{2}y-\frac{5}{2}x^{2}y^{3})$$

Factor out \frac{1}{30}.

$$\frac{22x^{2}y-75x^{2}y^{3}}{30}$$

Consider 22x^{2}y-75x^{2}y^{3}. Factor out x^{2}y.

$$x^{2}y\left(22-75y^{2}\right)$$

Rewrite the complete factored expression. Polynomial 22-75y^{2} is not factored since it does not have any rational roots.

$$\frac{x^{2}y\left(22-75y^{2}\right)}{30}$$

Evaluate

$$\frac{yx^{2}\left(22-75y^{2}\right)}{30}$$