Solve (1/4-3/2+1/20+1/5)^3-(-frac{1}{3}+1)^2+(frac{12}{5}-frac{3}{20}-frac{25}{12})^2

$$( \frac { 1 } { 4 } - \frac { 3 } { 2 } + \frac { 1 } { 20 } + \frac { 1 } { 5 } ) ^ { 3 } - ( - \frac { 1 } { 3 } + 1 ) ^ { 2 } + ( \frac { 12 } { 5 } - \frac { 3 } { 20 } - \frac { 25 } { 12 } ) ^ { 2 }$$

Evaluate

$$-\frac{17}{12}\approx -1.416666667$$

Solution Steps

Subtract \frac{3}{2} from \frac{1}{4} to get -\frac{5}{4}.

$$\left(-\frac{5}{4}+\frac{1}{20}+\frac{1}{5}\right)^{3}-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

Add -\frac{5}{4} and \frac{1}{20} to get -\frac{6}{5}.

$$\left(-\frac{6}{5}+\frac{1}{5}\right)^{3}-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

Add -\frac{6}{5} and \frac{1}{5} to get -1.

$$\left(-1\right)^{3}-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

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

$$-1-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

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

$$-1-\left(\frac{2}{3}\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

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

$$-1-\frac{4}{9}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

Subtract \frac{4}{9} from -1 to get -\frac{13}{9}.

$$-\frac{13}{9}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

Subtract \frac{3}{20} from \frac{12}{5} to get \frac{9}{4}.

$$-\frac{13}{9}+\left(\frac{9}{4}-\frac{25}{12}\right)^{2}$$

Subtract \frac{25}{12} from \frac{9}{4} to get \frac{1}{6}.

$$-\frac{13}{9}+\left(\frac{1}{6}\right)^{2}$$

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

$$-\frac{13}{9}+\frac{1}{36}$$

Add -\frac{13}{9} and \frac{1}{36} to get -\frac{17}{12}.

$$-\frac{17}{12}$$

Factor

$$-\frac{17}{12} = -1\frac{5}{12} = -1.4166666666666667$$