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

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

Evaluate

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

Short Solution Steps

Cancel out 4 and 4.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{a}{2} times \frac{3}{3}. Multiply \frac{2a^{2}}{3} times \frac{2}{2}.

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

Since \frac{3a}{6} and \frac{2\times 2a^{2}}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3a+2\times 2a^{2}.

$$\frac{3a+4a^{2}}{6}-a^{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{3} times \frac{6}{6}.

$$\frac{3a+4a^{2}}{6}-\frac{6a^{3}}{6}$$

Since \frac{3a+4a^{2}}{6} and \frac{6a^{3}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3a+4a^{2}-6a^{3}}{6}$$

Divide each term of 3a+4a^{2}-6a^{3} by 6 to get \frac{1}{2}a-a^{3}+\frac{2}{3}a^{2}.

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

Factor

$$-a\left(a-\left(-\frac{\sqrt{22}}{6}+\frac{1}{3}\right)\right)\left(a-\left(\frac{\sqrt{22}}{6}+\frac{1}{3}\right)\right)$$