Solve 1/2[12013-2014)^2+(2014-2015)^2+(2015-2013)^2]

$$\frac { 1 } { 2 } [ 12013 - 2014 ) ^ { 2 } + ( 2014 - 2015 ) ^ { 2 } + ( 2015 - 2013 ) ^ { 2 } ]$$

Evaluate

$$\frac{99980011}{2}=49990005.5$$

Solution Steps

Subtract 2014 from 12013 to get 9999.

$$\frac{1}{2}\times 9999^{2}+\left(2014-2015\right)^{2}+\left(2015-2013\right)^{2}$$

Calculate 9999 to the power of 2 and get 99980001.

$$\frac{1}{2}\times 99980001+\left(2014-2015\right)^{2}+\left(2015-2013\right)^{2}$$

Multiply \frac{1}{2} and 99980001 to get \frac{99980001}{2}.

$$\frac{99980001}{2}+\left(2014-2015\right)^{2}+\left(2015-2013\right)^{2}$$

Subtract 2015 from 2014 to get -1.

$$\frac{99980001}{2}+\left(-1\right)^{2}+\left(2015-2013\right)^{2}$$

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

$$\frac{99980001}{2}+1+\left(2015-2013\right)^{2}$$

Add \frac{99980001}{2} and 1 to get \frac{99980003}{2}.

$$\frac{99980003}{2}+\left(2015-2013\right)^{2}$$

Subtract 2013 from 2015 to get 2.

$$\frac{99980003}{2}+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{99980003}{2}+4$$

Add \frac{99980003}{2} and 4 to get \frac{99980011}{2}.

$$\frac{99980011}{2}$$

Factor

$$\frac{23 \cdot 1571 \cdot 2767}{2} = 49990005\frac{1}{2} = 49990005.5$$