Solve {left(2/5right)}^2-{left(-5/2right)}^2

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

Evaluate

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

Solution Steps

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

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

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

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

Least common multiple of 25 and 4 is 100. Convert \frac{4}{25} and \frac{25}{4} to fractions with denominator 100.

$$\frac{16}{100}-\frac{625}{100}$$

Since \frac{16}{100} and \frac{625}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-625}{100}$$

Subtract 625 from 16 to get -609.

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

Factor

$$-\frac{609}{100} = -6\frac{9}{100} = -6.09$$