Solve 9/16x^{4}+4/9y^{2}-x^{2}y-1/3y^{2}+x^{2}y+1/4x^{4}+frac{1}{6}x^2y-frac{1}{6}yx^2-frac{1}{9}y^2-2x^3}

$$\frac { 9 } { 16 } x ^ { 4 } + \frac { 4 } { 9 } y ^ { 2 } - x ^ { 2 } y - \frac { 1 } { 3 } y ^ { 2 } + x ^ { 2 } y + \frac { 1 } { 4 } x ^ { 4 } + \frac { 1 } { 6 } x ^ { 2 } y - \frac { 1 } { 6 } y x ^ { 2 } - \frac { 1 } { 9 } y ^ { 2 } - 2 x ^ { 3 } \}$$

Evaluate

$$\frac{13x^{4}}{16}-2x^{3}$$

Solution Steps

Combine x^{2}y and \frac{1}{6}x^{2}y to get \frac{7}{6}x^{2}y.

$$\frac{9}{16}x^{4}+\frac{4}{9}y^{2}-x^{2}y-\frac{1}{3}y^{2}+\frac{7}{6}x^{2}y+\frac{1}{4}x^{4}-\frac{1}{6}yx^{2}-\frac{1}{9}y^{2}-2x^{3}$$

Combine \frac{7}{6}x^{2}y and -\frac{1}{6}yx^{2} to get x^{2}y.

$$\frac{9}{16}x^{4}+\frac{4}{9}y^{2}-x^{2}y-\frac{1}{3}y^{2}+x^{2}y+\frac{1}{4}x^{4}-\frac{1}{9}y^{2}-2x^{3}$$

Combine -\frac{1}{3}y^{2} and -\frac{1}{9}y^{2} to get -\frac{4}{9}y^{2}.

$$\frac{9}{16}x^{4}+\frac{4}{9}y^{2}-x^{2}y-\frac{4}{9}y^{2}+x^{2}y+\frac{1}{4}x^{4}-2x^{3}$$

Combine \frac{4}{9}y^{2} and -\frac{4}{9}y^{2} to get 0.

$$\frac{9}{16}x^{4}-x^{2}y+x^{2}y+\frac{1}{4}x^{4}-2x^{3}$$

Combine -x^{2}y and x^{2}y to get 0.

$$\frac{9}{16}x^{4}+\frac{1}{4}x^{4}-2x^{3}$$

Combine \frac{9}{16}x^{4} and \frac{1}{4}x^{4} to get \frac{13}{16}x^{4}.

$$\frac{13}{16}x^{4}-2x^{3}$$

Factor

$$\frac{\left(13x-32\right)x^{3}}{16}$$

Solution Steps

Factor out \frac{1}{144}.

$$\frac{81x^{4}+64y^{2}-144x^{2}y-48y^{2}+144x^{2}y+36x^{4}+24x^{2}y-24yx^{2}-16y^{2}-288x^{3}}{144}$$

Consider 81x^{4}+64y^{2}-144x^{2}y-48y^{2}+144x^{2}y+36x^{4}+24x^{2}y-24yx^{2}-16y^{2}-288x^{3}. Multiply and combine like terms.

$$117x^{4}-288x^{3}$$

Consider 117x^{4}-288x^{3}. Factor out 9.

$$9\left(13x^{4}-32x^{3}\right)$$

Consider 13x^{4}-32x^{3}. Factor out x^{3}.

$$x^{3}\left(13x-32\right)$$

Rewrite the complete factored expression.

$$\frac{x^{3}\left(13x-32\right)}{16}$$

Simplify.

$$\frac{\left(13x-32\right)x^{3}}{16}$$