Solve [7/12-1/2-(-1/2)^{2}]^2-(-1/2)^2-[frac{4}{3}-(-1)^2]^2+frac{7}{12}

$$[ \frac { 7 } { 12 } - \frac { 1 } { 2 } - ( - \frac { 1 } { 2 } ) ^ { 2 } ] ^ { 2 } - ( - \frac { 1 } { 2 } ) ^ { 2 } - [ \frac { 4 } { 3 } - ( - 1 ) ^ { 2 } ] ^ { 2 } + \frac { 7 } { 12 }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Subtract \frac{1}{2} from \frac{7}{12} to get \frac{1}{12}.

$$\left(\frac{1}{12}-\left(-\frac{1}{2}\right)^{2}\right)^{2}-\left(-\frac{1}{2}\right)^{2}-\left(\frac{4}{3}-\left(-1\right)^{2}\right)^{2}+\frac{7}{12}$$

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

$$\left(\frac{1}{12}-\frac{1}{4}\right)^{2}-\left(-\frac{1}{2}\right)^{2}-\left(\frac{4}{3}-\left(-1\right)^{2}\right)^{2}+\frac{7}{12}$$

Subtract \frac{1}{4} from \frac{1}{12} to get -\frac{1}{6}.

$$\left(-\frac{1}{6}\right)^{2}-\left(-\frac{1}{2}\right)^{2}-\left(\frac{4}{3}-\left(-1\right)^{2}\right)^{2}+\frac{7}{12}$$

Calculate -\frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{1}{36}-\left(-\frac{1}{2}\right)^{2}-\left(\frac{4}{3}-\left(-1\right)^{2}\right)^{2}+\frac{7}{12}$$

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

$$\frac{1}{36}-\frac{1}{4}-\left(\frac{4}{3}-\left(-1\right)^{2}\right)^{2}+\frac{7}{12}$$

Subtract \frac{1}{4} from \frac{1}{36} to get -\frac{2}{9}.

$$-\frac{2}{9}-\left(\frac{4}{3}-\left(-1\right)^{2}\right)^{2}+\frac{7}{12}$$

Calculate -1 to the power of 2 and get 1.

$$-\frac{2}{9}-\left(\frac{4}{3}-1\right)^{2}+\frac{7}{12}$$

Subtract 1 from \frac{4}{3} to get \frac{1}{3}.

$$-\frac{2}{9}-\left(\frac{1}{3}\right)^{2}+\frac{7}{12}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$-\frac{2}{9}-\frac{1}{9}+\frac{7}{12}$$

Subtract \frac{1}{9} from -\frac{2}{9} to get -\frac{1}{3}.

$$-\frac{1}{3}+\frac{7}{12}$$

Add -\frac{1}{3} and \frac{7}{12} to get \frac{1}{4}.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$