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

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

Evaluate

$$-\frac{a^{2}}{5}+\frac{8a}{5}+1$$

Solution Steps

Combine \frac{4}{3}a and -2a to get -\frac{2}{3}a.

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

Use the distributive property to multiply \frac{3}{5} by -\frac{2}{3}a+\frac{1}{2}a^{2}-\frac{5}{2}.

$$-\frac{1}{2}a^{2}+2a+\frac{5}{2}-\frac{2}{5}a+\frac{3}{10}a^{2}-\frac{3}{2}$$

Combine 2a and -\frac{2}{5}a to get \frac{8}{5}a.

$$-\frac{1}{2}a^{2}+\frac{8}{5}a+\frac{5}{2}+\frac{3}{10}a^{2}-\frac{3}{2}$$

Combine -\frac{1}{2}a^{2} and \frac{3}{10}a^{2} to get -\frac{1}{5}a^{2}.

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

Subtract \frac{3}{2} from \frac{5}{2} to get 1.

$$-\frac{1}{5}a^{2}+\frac{8}{5}a+1$$

Expand

$$-\frac{a^{2}}{5}+\frac{8a}{5}+1$$

Solution Steps

Combine \frac{4}{3}a and -2a to get -\frac{2}{3}a.

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

Use the distributive property to multiply \frac{3}{5} by -\frac{2}{3}a+\frac{1}{2}a^{2}-\frac{5}{2}.

$$-\frac{1}{2}a^{2}+2a+\frac{5}{2}-\frac{2}{5}a+\frac{3}{10}a^{2}-\frac{3}{2}$$

Combine 2a and -\frac{2}{5}a to get \frac{8}{5}a.

$$-\frac{1}{2}a^{2}+\frac{8}{5}a+\frac{5}{2}+\frac{3}{10}a^{2}-\frac{3}{2}$$

Combine -\frac{1}{2}a^{2} and \frac{3}{10}a^{2} to get -\frac{1}{5}a^{2}.

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

Subtract \frac{3}{2} from \frac{5}{2} to get 1.

$$-\frac{1}{5}a^{2}+\frac{8}{5}a+1$$