Solve 2/3a-1/4a^2+1/4a+1/2a^2=

$$\frac { 2 } { 3 } a - \frac { 1 } { 4 } a ^ { 2 } + \frac { 1 } { 4 } a + \frac { 1 } { 2 } a ^ { 2 } =$$

Evaluate

$$\frac{a\left(3a+11\right)}{12}$$

Solution Steps

Combine \frac{2}{3}a and \frac{1}{4}a to get \frac{11}{12}a.

$$\frac{11}{12}a-\frac{1}{4}a^{2}+\frac{1}{2}a^{2}$$

Combine -\frac{1}{4}a^{2} and \frac{1}{2}a^{2} to get \frac{1}{4}a^{2}.

$$\frac{11}{12}a+\frac{1}{4}a^{2}$$

Factor

$$\frac{a\left(3a+11\right)}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{8a-3a^{2}+3a+6a^{2}}{12}$$

Consider 8a-3a^{2}+3a+6a^{2}. Factor out a.

$$a\left(11+3a\right)$$

Consider 8-3a+3+6a. Multiply and combine like terms.

$$3a+11$$

Rewrite the complete factored expression.

$$\frac{a\left(3a+11\right)}{12}$$