Solve left(77-85.5right)^2+left(82-85.5right)^2+left(86-85.5right)^2+left(78-85.5right)^2+{left(81-85.5right)}^2+{left(86-85.5right)}^2+{left(77-85.5right)}^2+{left(81-85.5right)}^2

$${ \left(77-85.5 \right) }^{ 2 } + { \left(82-85.5 \right) }^{ 2 } + { \left(86-85.5 \right) }^{ 2 } + { \left(78-85.5 \right) }^{ 2 } + { \left(81-85.5 \right) }^{ 2 } + { \left(86-85.5 \right) }^{ 2 } + { \left(77-85.5 \right) }^{ 2 } + { \left(81-85.5 \right) }^{ 2 }$$

Evaluate

$$254$$

Solution Steps

Subtract 85.5 from 77 to get -8.5.

$$\left(-8.5\right)^{2}+\left(82-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Calculate -8.5 to the power of 2 and get 72.25.

$$72.25+\left(82-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Subtract 85.5 from 82 to get -3.5.

$$72.25+\left(-3.5\right)^{2}+\left(86-85.5\right)^{2}+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Calculate -3.5 to the power of 2 and get 12.25.

$$72.25+12.25+\left(86-85.5\right)^{2}+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Add 72.25 and 12.25 to get 84.5.

$$84.5+\left(86-85.5\right)^{2}+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Subtract 85.5 from 86 to get 0.5.

$$84.5+0.5^{2}+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$84.5+0.25+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Add 84.5 and 0.25 to get 84.75.

$$84.75+\left(78-85.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Subtract 85.5 from 78 to get -7.5.

$$84.75+\left(-7.5\right)^{2}+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Calculate -7.5 to the power of 2 and get 56.25.

$$84.75+56.25+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Add 84.75 and 56.25 to get 141.

$$141+\left(81-85.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Subtract 85.5 from 81 to get -4.5.

$$141+\left(-4.5\right)^{2}+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Calculate -4.5 to the power of 2 and get 20.25.

$$141+20.25+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Add 141 and 20.25 to get 161.25.

$$161.25+\left(86-85.5\right)^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Subtract 85.5 from 86 to get 0.5.

$$161.25+0.5^{2}+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$161.25+0.25+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Add 161.25 and 0.25 to get 161.5.

$$161.5+\left(77-85.5\right)^{2}+\left(81-85.5\right)^{2}$$

Subtract 85.5 from 77 to get -8.5.

$$161.5+\left(-8.5\right)^{2}+\left(81-85.5\right)^{2}$$

Calculate -8.5 to the power of 2 and get 72.25.

$$161.5+72.25+\left(81-85.5\right)^{2}$$

Add 161.5 and 72.25 to get 233.75.

$$233.75+\left(81-85.5\right)^{2}$$

Subtract 85.5 from 81 to get -4.5.

$$233.75+\left(-4.5\right)^{2}$$

Calculate -4.5 to the power of 2 and get 20.25.

$$233.75+20.25$$

Add 233.75 and 20.25 to get 254.

$$254$$

Factor

$$2\times 127$$