Solve (51/2)^2-(41/2)^2

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

Evaluate

$$10$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\left(\frac{10+1}{2}\right)^{2}-\left(\frac{4\times 2+1}{2}\right)^{2}$$

Add 10 and 1 to get 11.

$$\left(\frac{11}{2}\right)^{2}-\left(\frac{4\times 2+1}{2}\right)^{2}$$

Calculate \frac{11}{2} to the power of 2 and get \frac{121}{4}.

$$\frac{121}{4}-\left(\frac{4\times 2+1}{2}\right)^{2}$$

Multiply 4 and 2 to get 8.

$$\frac{121}{4}-\left(\frac{8+1}{2}\right)^{2}$$

Add 8 and 1 to get 9.

$$\frac{121}{4}-\left(\frac{9}{2}\right)^{2}$$

Calculate \frac{9}{2} to the power of 2 and get \frac{81}{4}.

$$\frac{121}{4}-\frac{81}{4}$$

Subtract \frac{81}{4} from \frac{121}{4} to get 10.

$$10$$

Factor

$$2\times 5$$