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

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

Verify

Solution Steps

Multiply -3 and 2 to get -6.

$$-6\times 4+2\left(-\frac{1}{2}\right)\times 3\times \frac{1}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Multiply -6 and 4 to get -24.

$$-24+2\left(-\frac{1}{2}\right)\times 3\times \frac{1}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Cancel out 2 and 2.

$$-24-3\times \frac{1}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Multiply -3 and \frac{1}{2} to get \frac{-3}{2}.

$$-24+\frac{-3}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

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

$$-24-\frac{3}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Convert -24 to fraction -\frac{48}{2}.

$$-\frac{48}{2}-\frac{3}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Since -\frac{48}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-48-3}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Subtract 3 from -48 to get -51.

$$-\frac{51}{2}-2\left(-\frac{1}{2}\right)^{2}=4\times \left(\frac{1}{2}\right)^{2}$$

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

$$-\frac{51}{2}-2\times \frac{1}{4}=4\times \left(\frac{1}{2}\right)^{2}$$

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

$$-\frac{51}{2}-\frac{2}{4}=4\times \left(\frac{1}{2}\right)^{2}$$

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

$$-\frac{51}{2}-\frac{1}{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Since -\frac{51}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-51-1}{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Subtract 1 from -51 to get -52.

$$\frac{-52}{2}=4\times \left(\frac{1}{2}\right)^{2}$$

Divide -52 by 2 to get -26.

$$-26=4\times \left(\frac{1}{2}\right)^{2}$$

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

$$-26=4\times \frac{1}{4}$$

Cancel out 4 and 4.

$$-26=1$$

Compare -26 and 1.

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