Solve -1/6a^3-2/3x^2-y+1+1/3a^3-5/6x^2-frac{1}{2}y-2

$$- \frac { 1 } { 6 } a ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } - y + 1 + \frac { 1 } { 3 } a ^ { 3 } - \frac { 5 } { 6 } x ^ { 2 } - \frac { 1 } { 2 } y - 2$$

Evaluate

$$\frac{a^{3}}{6}-\frac{3x^{2}}{2}-\frac{3y}{2}-1$$

Solution Steps

Combine -\frac{1}{6}a^{3} and \frac{1}{3}a^{3} to get \frac{1}{6}a^{3}.

$$\frac{1}{6}a^{3}-\frac{2}{3}x^{2}-y+1-\frac{5}{6}x^{2}-\frac{1}{2}y-2$$

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

$$\frac{1}{6}a^{3}-\frac{3}{2}x^{2}-y+1-\frac{1}{2}y-2$$

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

$$\frac{1}{6}a^{3}-\frac{3}{2}x^{2}-\frac{3}{2}y+1-2$$

Subtract 2 from 1 to get -1.

$$\frac{1}{6}a^{3}-\frac{3}{2}x^{2}-\frac{3}{2}y-1$$

Factor

$$\frac{-9x^{2}-9y+a^{3}-6}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{a^{3}-9x^{2}-9y-6}{6}$$