Solve 6a-16a^2/3+2a/3

$$6 a - \frac { 16 a ^ { 2 } } { 3 } + \frac { 2 a } { 3 }$$

Evaluate

$$\frac{4a\left(5-4a\right)}{3}$$

Short Solution Steps

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

$$\frac{3\times 6a}{3}-\frac{16a^{2}}{3}+\frac{2a}{3}$$

Since \frac{3\times 6a}{3} and \frac{16a^{2}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 6a-16a^{2}}{3}+\frac{2a}{3}$$

Do the multiplications in 3\times 6a-16a^{2}.

$$\frac{18a-16a^{2}}{3}+\frac{2a}{3}$$

Since \frac{18a-16a^{2}}{3} and \frac{2a}{3} have the same denominator, add them by adding their numerators.

$$\frac{18a-16a^{2}+2a}{3}$$

Combine like terms in 18a-16a^{2}+2a.

$$\frac{20a-16a^{2}}{3}$$

Factor

$$\frac{4a\left(5-4a\right)}{3}$$

Solution Steps

Factor out \frac{2}{3}.

$$\frac{2\left(9a-8a^{2}+a\right)}{3}$$

Consider 9a-8a^{2}+a. Factor out a.

$$a\left(10-8a\right)$$

Consider 9-8a+1. Multiply and combine like terms.

$$-8a+10$$

Consider -8a+10. Factor out 2.

$$2\left(-4a+5\right)$$

Rewrite the complete factored expression.

$$\frac{4a\left(-4a+5\right)}{3}$$