Solve (-2/5a^3+1/6a^2-2ab)+(-3/4a^2+a^3-1/3ab)-(frac{1}{12}{a}^2-frac{7}{3}ab)

$$(- \frac{ 2 }{ 5 } { a }^{ 3 } + \frac{ 1 }{ 6 } { a }^{ 2 } -2ab)+(- \frac{ 3 }{ 4 } { a }^{ 2 } + { a }^{ 3 } - \frac{ 1 }{ 3 } ab)-( \frac{ 1 }{ 12 } { a }^{ 2 } - \frac{ 7 }{ 3 } ab)$$

Evaluate

$$\frac{3a^{3}}{5}-\frac{2a^{2}}{3}$$

Solution Steps

Combine \frac{1}{6}a^{2} and -\frac{3}{4}a^{2} to get -\frac{7}{12}a^{2}.

$$-\frac{2}{5}a^{3}-\frac{7}{12}a^{2}-2ab+a^{3}-\frac{1}{3}ab-\left(\frac{1}{12}a^{2}-\frac{7}{3}ab\right)$$

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

$$\frac{3}{5}a^{3}-\frac{7}{12}a^{2}-2ab-\frac{1}{3}ab-\left(\frac{1}{12}a^{2}-\frac{7}{3}ab\right)$$

Combine -2ab and -\frac{1}{3}ab to get -\frac{7}{3}ab.

$$\frac{3}{5}a^{3}-\frac{7}{12}a^{2}-\frac{7}{3}ab-\left(\frac{1}{12}a^{2}-\frac{7}{3}ab\right)$$

To find the opposite of \frac{1}{12}a^{2}-\frac{7}{3}ab, find the opposite of each term.

$$\frac{3}{5}a^{3}-\frac{7}{12}a^{2}-\frac{7}{3}ab-\frac{1}{12}a^{2}+\frac{7}{3}ab$$

Combine -\frac{7}{12}a^{2} and -\frac{1}{12}a^{2} to get -\frac{2}{3}a^{2}.

$$\frac{3}{5}a^{3}-\frac{2}{3}a^{2}-\frac{7}{3}ab+\frac{7}{3}ab$$

Combine -\frac{7}{3}ab and \frac{7}{3}ab to get 0.

$$\frac{3}{5}a^{3}-\frac{2}{3}a^{2}$$

Expand

$$\frac{3a^{3}}{5}-\frac{2a^{2}}{3}$$

Solution Steps

Combine \frac{1}{6}a^{2} and -\frac{3}{4}a^{2} to get -\frac{7}{12}a^{2}.

$$-\frac{2}{5}a^{3}-\frac{7}{12}a^{2}-2ab+a^{3}-\frac{1}{3}ab-\left(\frac{1}{12}a^{2}-\frac{7}{3}ab\right)$$

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

$$\frac{3}{5}a^{3}-\frac{7}{12}a^{2}-2ab-\frac{1}{3}ab-\left(\frac{1}{12}a^{2}-\frac{7}{3}ab\right)$$

Combine -2ab and -\frac{1}{3}ab to get -\frac{7}{3}ab.

$$\frac{3}{5}a^{3}-\frac{7}{12}a^{2}-\frac{7}{3}ab-\left(\frac{1}{12}a^{2}-\frac{7}{3}ab\right)$$

To find the opposite of \frac{1}{12}a^{2}-\frac{7}{3}ab, find the opposite of each term.

$$\frac{3}{5}a^{3}-\frac{7}{12}a^{2}-\frac{7}{3}ab-\frac{1}{12}a^{2}+\frac{7}{3}ab$$

Combine -\frac{7}{12}a^{2} and -\frac{1}{12}a^{2} to get -\frac{2}{3}a^{2}.

$$\frac{3}{5}a^{3}-\frac{2}{3}a^{2}-\frac{7}{3}ab+\frac{7}{3}ab$$

Combine -\frac{7}{3}ab and \frac{7}{3}ab to get 0.

$$\frac{3}{5}a^{3}-\frac{2}{3}a^{2}$$