Solve 4(-1/2)^3-2(-1/2)^2+3(-1/2)+(-1)^3

$$4 ( - \frac { 1 } { 2 } ) ^ { 3 } - 2 ( - \frac { 1 } { 2 } ) ^ { 2 } + 3 ( - \frac { 1 } { 2 } ) + ( - 1 ) ^ { 3 }$$

Evaluate

$$-\frac{7}{2}=-3.5$$

Solution Steps

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$4\left(-\frac{1}{8}\right)-2\left(-\frac{1}{2}\right)^{2}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Express 4\left(-\frac{1}{8}\right) as a single fraction.

$$\frac{4\left(-1\right)}{8}-2\left(-\frac{1}{2}\right)^{2}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Multiply 4 and -1 to get -4.

$$\frac{-4}{8}-2\left(-\frac{1}{2}\right)^{2}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{2}-2\left(-\frac{1}{2}\right)^{2}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-\frac{1}{2}-2\times \frac{1}{4}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$-\frac{1}{2}-\frac{2}{4}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}-\frac{1}{2}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Since -\frac{1}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-1}{2}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Subtract 1 from -1 to get -2.

$$\frac{-2}{2}+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Divide -2 by 2 to get -1.

$$-1+3\left(-\frac{1}{2}\right)+\left(-1\right)^{3}$$

Express 3\left(-\frac{1}{2}\right) as a single fraction.

$$-1+\frac{3\left(-1\right)}{2}+\left(-1\right)^{3}$$

Multiply 3 and -1 to get -3.

$$-1+\frac{-3}{2}+\left(-1\right)^{3}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-1-\frac{3}{2}+\left(-1\right)^{3}$$

Convert -1 to fraction -\frac{2}{2}.

$$-\frac{2}{2}-\frac{3}{2}+\left(-1\right)^{3}$$

Since -\frac{2}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-3}{2}+\left(-1\right)^{3}$$

Subtract 3 from -2 to get -5.

$$-\frac{5}{2}+\left(-1\right)^{3}$$

Calculate -1 to the power of 3 and get -1.

$$-\frac{5}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{5}{2}-\frac{2}{2}$$

Since -\frac{5}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-2}{2}$$

Subtract 2 from -5 to get -7.

$$-\frac{7}{2}$$

Factor

$$-\frac{7}{2} = -3\frac{1}{2} = -3.5$$