Solve left(-1-2right)^2+{left(2-1/2right)}^2-{left(-1-1/2right)}^2

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

Evaluate

$$9$$

Solution Steps

Subtract 2 from -1 to get -3.

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

Calculate -3 to the power of 2 and get 9.

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

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

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

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

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

Add 9 and \frac{9}{4} to get \frac{45}{4}.

$$\frac{45}{4}-\left(-1-\frac{1}{2}\right)^{2}$$

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

$$\frac{45}{4}-\left(-\frac{3}{2}\right)^{2}$$

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

$$\frac{45}{4}-\frac{9}{4}$$

Subtract \frac{9}{4} from \frac{45}{4} to get 9.

$$9$$

Factor

$$3^{2}$$