Solve (-2a^{2}+8/15ab-2/5b^{2})-[-3a^2-(-1/5b^2--6/5ab)]+(a^2+frac{3}{5}b^2)

$$( - 2 a ^ { 2 } + \frac { 8 } { 15 } a b - \frac { 2 } { 5 } b ^ { 2 } ) - [ - 3 a ^ { 2 } - ( - \frac { 1 } { 5 } b ^ { 2 } - \frac { - 6 } { 5 } a b ) ] + ( a ^ { 2 } + \frac { 3 } { 5 } b ^ { 2 } )$$

Evaluate

$$\frac{26ab}{15}+2a^{2}$$

Solution Steps

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\left(-3a^{2}-\left(-\frac{1}{5}b^{2}-\left(-\frac{6}{5}ab\right)\right)\right)+a^{2}+\frac{3}{5}b^{2}$$

The opposite of -\frac{6}{5}ab is \frac{6}{5}ab.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\left(-3a^{2}-\left(-\frac{1}{5}b^{2}+\frac{6}{5}ab\right)\right)+a^{2}+\frac{3}{5}b^{2}$$

To find the opposite of -\frac{1}{5}b^{2}+\frac{6}{5}ab, find the opposite of each term.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\left(-3a^{2}+\frac{1}{5}b^{2}-\frac{6}{5}ab\right)+a^{2}+\frac{3}{5}b^{2}$$

To find the opposite of -3a^{2}+\frac{1}{5}b^{2}-\frac{6}{5}ab, find the opposite of each term.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}+3a^{2}-\frac{1}{5}b^{2}+\frac{6}{5}ab+a^{2}+\frac{3}{5}b^{2}$$

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

$$a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\frac{1}{5}b^{2}+\frac{6}{5}ab+a^{2}+\frac{3}{5}b^{2}$$

Combine -\frac{2}{5}b^{2} and -\frac{1}{5}b^{2} to get -\frac{3}{5}b^{2}.

$$a^{2}+\frac{8}{15}ab-\frac{3}{5}b^{2}+\frac{6}{5}ab+a^{2}+\frac{3}{5}b^{2}$$

Combine \frac{8}{15}ab and \frac{6}{5}ab to get \frac{26}{15}ab.

$$a^{2}+\frac{26}{15}ab-\frac{3}{5}b^{2}+a^{2}+\frac{3}{5}b^{2}$$

Combine a^{2} and a^{2} to get 2a^{2}.

$$2a^{2}+\frac{26}{15}ab-\frac{3}{5}b^{2}+\frac{3}{5}b^{2}$$

Combine -\frac{3}{5}b^{2} and \frac{3}{5}b^{2} to get 0.

$$2a^{2}+\frac{26}{15}ab$$

Expand

$$\frac{26ab}{15}+2a^{2}$$

Solution Steps

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\left(-3a^{2}-\left(-\frac{1}{5}b^{2}-\left(-\frac{6}{5}ab\right)\right)\right)+a^{2}+\frac{3}{5}b^{2}$$

The opposite of -\frac{6}{5}ab is \frac{6}{5}ab.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\left(-3a^{2}-\left(-\frac{1}{5}b^{2}+\frac{6}{5}ab\right)\right)+a^{2}+\frac{3}{5}b^{2}$$

To find the opposite of -\frac{1}{5}b^{2}+\frac{6}{5}ab, find the opposite of each term.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\left(-3a^{2}+\frac{1}{5}b^{2}-\frac{6}{5}ab\right)+a^{2}+\frac{3}{5}b^{2}$$

To find the opposite of -3a^{2}+\frac{1}{5}b^{2}-\frac{6}{5}ab, find the opposite of each term.

$$-2a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}+3a^{2}-\frac{1}{5}b^{2}+\frac{6}{5}ab+a^{2}+\frac{3}{5}b^{2}$$

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

$$a^{2}+\frac{8}{15}ab-\frac{2}{5}b^{2}-\frac{1}{5}b^{2}+\frac{6}{5}ab+a^{2}+\frac{3}{5}b^{2}$$

Combine -\frac{2}{5}b^{2} and -\frac{1}{5}b^{2} to get -\frac{3}{5}b^{2}.

$$a^{2}+\frac{8}{15}ab-\frac{3}{5}b^{2}+\frac{6}{5}ab+a^{2}+\frac{3}{5}b^{2}$$

Combine \frac{8}{15}ab and \frac{6}{5}ab to get \frac{26}{15}ab.

$$a^{2}+\frac{26}{15}ab-\frac{3}{5}b^{2}+a^{2}+\frac{3}{5}b^{2}$$

Combine a^{2} and a^{2} to get 2a^{2}.

$$2a^{2}+\frac{26}{15}ab-\frac{3}{5}b^{2}+\frac{3}{5}b^{2}$$

Combine -\frac{3}{5}b^{2} and \frac{3}{5}b^{2} to get 0.

$$2a^{2}+\frac{26}{15}ab$$