Solve left(1200-1400right)^2+left(1300-1400right)^2+left(1400-1400right)^2+left(1500-1400right)^2+{left(1600-1400right)}^2

$${ \left(1200-1400 \right) }^{ 2 } + { \left(1300-1400 \right) }^{ 2 } + { \left(1400-1400 \right) }^{ 2 } + { \left(1500-1400 \right) }^{ 2 } + { \left(1600-1400 \right) }^{ 2 }$$

Evaluate

$$100000$$

Solution Steps

Subtract 1400 from 1200 to get -200.

$$\left(-200\right)^{2}+\left(1300-1400\right)^{2}+\left(1400-1400\right)^{2}+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Calculate -200 to the power of 2 and get 40000.

$$40000+\left(1300-1400\right)^{2}+\left(1400-1400\right)^{2}+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Subtract 1400 from 1300 to get -100.

$$40000+\left(-100\right)^{2}+\left(1400-1400\right)^{2}+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Calculate -100 to the power of 2 and get 10000.

$$40000+10000+\left(1400-1400\right)^{2}+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Add 40000 and 10000 to get 50000.

$$50000+\left(1400-1400\right)^{2}+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Subtract 1400 from 1400 to get 0.

$$50000+0^{2}+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Calculate 0 to the power of 2 and get 0.

$$50000+0+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Add 50000 and 0 to get 50000.

$$50000+\left(1500-1400\right)^{2}+\left(1600-1400\right)^{2}$$

Subtract 1400 from 1500 to get 100.

$$50000+100^{2}+\left(1600-1400\right)^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$50000+10000+\left(1600-1400\right)^{2}$$

Add 50000 and 10000 to get 60000.

$$60000+\left(1600-1400\right)^{2}$$

Subtract 1400 from 1600 to get 200.

$$60000+200^{2}$$

Calculate 200 to the power of 2 and get 40000.

$$60000+40000$$

Add 60000 and 40000 to get 100000.

$$100000$$

Factor

$$2^{5}\times 5^{5}$$