Solve (-23/6)^2-(2/5)^2

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

Evaluate

$$\frac{609}{100}=6.09$$

Solution Steps

Multiply 2 and 6 to get 12.

$$\left(-\frac{12+3}{6}\right)^{2}-\left(\frac{2}{5}\right)^{2}$$

Add 12 and 3 to get 15.

$$\left(-\frac{15}{6}\right)^{2}-\left(\frac{2}{5}\right)^{2}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\left(-\frac{5}{2}\right)^{2}-\left(\frac{2}{5}\right)^{2}$$

Calculate -\frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}-\left(\frac{2}{5}\right)^{2}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{25}{4}-\frac{4}{25}$$

Subtract \frac{4}{25} from \frac{25}{4} to get \frac{609}{100}.

$$\frac{609}{100}$$

Factor

$$\frac{3 \cdot 7 \cdot 29}{2 ^ {2} \cdot 5 ^ {2}} = 6\frac{9}{100} = 6.09$$