Solve (991/2)^2-(1/2)^2

$$( 99 \frac { 1 } { 2 } ) ^ { 2 } - ( \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$9900$$

Solution Steps

Multiply 99 and 2 to get 198.

$$\left(\frac{198+1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{2}$$

Add 198 and 1 to get 199.

$$\left(\frac{199}{2}\right)^{2}-\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{199}{2} to the power of 2 and get \frac{39601}{4}.

$$\frac{39601}{4}-\left(\frac{1}{2}\right)^{2}$$

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

$$\frac{39601}{4}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{39601}{4} to get 9900.

$$9900$$

Factor

$$2^{2}\times 3^{2}\times 5^{2}\times 11$$