Solve {left(3/2right)}^2-{left(9/10right)}^2

$${ \left( \frac{ 3 }{ 2 } \right) }^{ 2 } - { \left( \frac{ 9 }{ 10 } \right) }^{ 2 }$$

Evaluate

$$\frac{36}{25}=1.44$$

Solution Steps

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

$$\frac{9}{4}-\left(\frac{9}{10}\right)^{2}$$

Calculate \frac{9}{10} to the power of 2 and get \frac{81}{100}.

$$\frac{9}{4}-\frac{81}{100}$$

Least common multiple of 4 and 100 is 100. Convert \frac{9}{4} and \frac{81}{100} to fractions with denominator 100.

$$\frac{225}{100}-\frac{81}{100}$$

Since \frac{225}{100} and \frac{81}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{225-81}{100}$$

Subtract 81 from 225 to get 144.

$$\frac{144}{100}$$

Reduce the fraction \frac{144}{100} to lowest terms by extracting and canceling out 4.

$$\frac{36}{25}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {2}}{5 ^ {2}} = 1\frac{11}{25} = 1.44$$