Solve 1/2[(2011-2012)^2+(2012-2013)^2+(2013-2011)^2]

$$\frac { 1 } { 2 } [ ( 2011 - 2012 ) ^ { 2 } + ( 2012 - 2013 ) ^ { 2 } + ( 2013 - 2011 ) ^ { 2 } ]$$

Evaluate

$$3$$

Solution Steps

Subtract 2012 from 2011 to get -1.

$$\frac{1}{2}\left(\left(-1\right)^{2}+\left(2012-2013\right)^{2}+\left(2013-2011\right)^{2}\right)$$

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

$$\frac{1}{2}\left(1+\left(2012-2013\right)^{2}+\left(2013-2011\right)^{2}\right)$$

Subtract 2013 from 2012 to get -1.

$$\frac{1}{2}\left(1+\left(-1\right)^{2}+\left(2013-2011\right)^{2}\right)$$

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

$$\frac{1}{2}\left(1+1+\left(2013-2011\right)^{2}\right)$$

Add 1 and 1 to get 2.

$$\frac{1}{2}\left(2+\left(2013-2011\right)^{2}\right)$$

Subtract 2011 from 2013 to get 2.

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

Calculate 2 to the power of 2 and get 4.

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

Add 2 and 4 to get 6.

$$\frac{1}{2}\times 6$$

Multiply \frac{1}{2} and 6 to get 3.

$$3$$

Factor

$$3$$