Solve [z-z^2/3]_1^0

$$[ z - \frac { z ^ { 2 } } { 3 } ] _ { 1 } ^ { 0 }$$

Evaluate

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

Solution Steps

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

$$\frac{3z}{3}-\frac{z^{2}}{3}$$

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

$$\frac{3z-z^{2}}{3}$$

Factor

$$\frac{z\left(3-z\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{3z-z^{2}}{3}$$

Consider 3z-z^{2}. Factor out z.

$$z\left(3-z\right)$$

Rewrite the complete factored expression.

$$\frac{z\left(-z+3\right)}{3}$$