Solve (1+1/2)^2-(1-1/2)^2

$$( 1 + \frac { 1 } { 2 } ) ^ { 2 } - ( 1 - \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$2$$

Solution Steps

Add 1 and \frac{1}{2} to get \frac{3}{2}.

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

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}-\left(1-\frac{1}{2}\right)^{2}$$

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

$$\frac{9}{4}-\left(\frac{1}{2}\right)^{2}$$

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

$$\frac{9}{4}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{9}{4} to get 2.

$$2$$

Factor

$$2$$