Solve (3/7a^2+1/3ab-3/5b^2)-(5/14a^2+frac{1}{2}ab-frac{1}{8})

$$( \frac { 3 } { 7 } a ^ { 2 } + \frac { 1 } { 3 } a b - \frac { 3 } { 5 } b ^ { 2 } ) - ( \frac { 5 } { 14 } a ^ { 2 } + \frac { 1 } { 2 } a b - \frac { 1 } { 8 } )$$

Evaluate

$$-\frac{ab}{6}+\frac{a^{2}}{14}-\frac{3b^{2}}{5}+\frac{1}{8}$$

Solution Steps

To find the opposite of \frac{5}{14}a^{2}+\frac{1}{2}ab-\frac{1}{8}, find the opposite of each term.

$$\frac{3}{7}a^{2}+\frac{1}{3}ab-\frac{3}{5}b^{2}-\frac{5}{14}a^{2}-\frac{1}{2}ab+\frac{1}{8}$$

Combine \frac{3}{7}a^{2} and -\frac{5}{14}a^{2} to get \frac{1}{14}a^{2}.

$$\frac{1}{14}a^{2}+\frac{1}{3}ab-\frac{3}{5}b^{2}-\frac{1}{2}ab+\frac{1}{8}$$

Combine \frac{1}{3}ab and -\frac{1}{2}ab to get -\frac{1}{6}ab.

$$\frac{1}{14}a^{2}-\frac{1}{6}ab-\frac{3}{5}b^{2}+\frac{1}{8}$$

Expand

$$-\frac{ab}{6}+\frac{a^{2}}{14}-\frac{3b^{2}}{5}+\frac{1}{8}$$

Solution Steps

To find the opposite of \frac{5}{14}a^{2}+\frac{1}{2}ab-\frac{1}{8}, find the opposite of each term.

$$\frac{3}{7}a^{2}+\frac{1}{3}ab-\frac{3}{5}b^{2}-\frac{5}{14}a^{2}-\frac{1}{2}ab+\frac{1}{8}$$

Combine \frac{3}{7}a^{2} and -\frac{5}{14}a^{2} to get \frac{1}{14}a^{2}.

$$\frac{1}{14}a^{2}+\frac{1}{3}ab-\frac{3}{5}b^{2}-\frac{1}{2}ab+\frac{1}{8}$$

Combine \frac{1}{3}ab and -\frac{1}{2}ab to get -\frac{1}{6}ab.

$$\frac{1}{14}a^{2}-\frac{1}{6}ab-\frac{3}{5}b^{2}+\frac{1}{8}$$