Solve (3/2)^3-3*(3/2)^2+3/2

$$( \frac { 3 } { 2 } ) ^ { 3 } - 3 \cdot ( \frac { 3 } { 2 } ) ^ { 2 } + \frac { 3 } { 2 }$$

Evaluate

$$-\frac{15}{8}=-1.875$$

Solution Steps

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{27}{8}-3\times \left(\frac{3}{2}\right)^{2}+\frac{3}{2}$$

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

$$\frac{27}{8}-3\times \frac{9}{4}+\frac{3}{2}$$

Express 3\times \frac{9}{4} as a single fraction.

$$\frac{27}{8}-\frac{3\times 9}{4}+\frac{3}{2}$$

Multiply 3 and 9 to get 27.

$$\frac{27}{8}-\frac{27}{4}+\frac{3}{2}$$

Least common multiple of 8 and 4 is 8. Convert \frac{27}{8} and \frac{27}{4} to fractions with denominator 8.

$$\frac{27}{8}-\frac{54}{8}+\frac{3}{2}$$

Since \frac{27}{8} and \frac{54}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-54}{8}+\frac{3}{2}$$

Subtract 54 from 27 to get -27.

$$-\frac{27}{8}+\frac{3}{2}$$

Least common multiple of 8 and 2 is 8. Convert -\frac{27}{8} and \frac{3}{2} to fractions with denominator 8.

$$-\frac{27}{8}+\frac{12}{8}$$

Since -\frac{27}{8} and \frac{12}{8} have the same denominator, add them by adding their numerators.

$$\frac{-27+12}{8}$$

Add -27 and 12 to get -15.

$$-\frac{15}{8}$$

Factor

$$-\frac{15}{8} = -1\frac{7}{8} = -1.875$$