Solve 2/3(3/4-1/2)^2-1/6(frac{5}{6}-frac{1}{3})^2

$$\frac { 2 } { 3 } ( \frac { 3 } { 4 } - \frac { 1 } { 2 } ) ^ { 2 } - \frac { 1 } { 6 } ( \frac { 5 } { 6 } - \frac { 1 } { 3 } ) ^ { 2 }$$

Evaluate

$$0$$

Solution Steps

Subtract \frac{1}{2} from \frac{3}{4} to get \frac{1}{4}.

$$\frac{2}{3}\times \left(\frac{1}{4}\right)^{2}-\frac{1}{6}\left(\frac{5}{6}-\frac{1}{3}\right)^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{2}{3}\times \frac{1}{16}-\frac{1}{6}\left(\frac{5}{6}-\frac{1}{3}\right)^{2}$$

Multiply \frac{2}{3} and \frac{1}{16} to get \frac{1}{24}.

$$\frac{1}{24}-\frac{1}{6}\left(\frac{5}{6}-\frac{1}{3}\right)^{2}$$

Subtract \frac{1}{3} from \frac{5}{6} to get \frac{1}{2}.

$$\frac{1}{24}-\frac{1}{6}\times \left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{24}-\frac{1}{6}\times \frac{1}{4}$$

Multiply \frac{1}{6} and \frac{1}{4} to get \frac{1}{24}.

$$\frac{1}{24}-\frac{1}{24}$$

Subtract \frac{1}{24} from \frac{1}{24} to get 0.

$$0$$

Factor

$$0$$