Solve left(88-85.5right)^2+left(94-85.5right)^2+left(93-85.5right)^2+left(90-85.5right)^2+{left(91-85.5right)}^2+{left(94-85.5right)}^2+{left(90-85.5right)}^2+{left(87-85.5right)}^2

$${ \left(88-85.5 \right) }^{ 2 } + { \left(94-85.5 \right) }^{ 2 } + { \left(93-85.5 \right) }^{ 2 } + { \left(90-85.5 \right) }^{ 2 } + { \left(91-85.5 \right) }^{ 2 } + { \left(94-85.5 \right) }^{ 2 } + { \left(90-85.5 \right) }^{ 2 } + { \left(87-85.5 \right) }^{ 2 }$$

Evaluate

$$280$$

Solution Steps

Subtract 85.5 from 88 to get 2.5.

$$2.5^{2}+\left(94-85.5\right)^{2}+\left(93-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Calculate 2.5 to the power of 2 and get 6.25.

$$6.25+\left(94-85.5\right)^{2}+\left(93-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Subtract 85.5 from 94 to get 8.5.

$$6.25+8.5^{2}+\left(93-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Calculate 8.5 to the power of 2 and get 72.25.

$$6.25+72.25+\left(93-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Add 6.25 and 72.25 to get 78.5.

$$78.5+\left(93-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Subtract 85.5 from 93 to get 7.5.

$$78.5+7.5^{2}+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Calculate 7.5 to the power of 2 and get 56.25.

$$78.5+56.25+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Add 78.5 and 56.25 to get 134.75.

$$134.75+\left(90-85.5\right)^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Subtract 85.5 from 90 to get 4.5.

$$134.75+4.5^{2}+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Calculate 4.5 to the power of 2 and get 20.25.

$$134.75+20.25+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Add 134.75 and 20.25 to get 155.

$$155+\left(91-85.5\right)^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Subtract 85.5 from 91 to get 5.5.

$$155+5.5^{2}+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Calculate 5.5 to the power of 2 and get 30.25.

$$155+30.25+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Add 155 and 30.25 to get 185.25.

$$185.25+\left(94-85.5\right)^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Subtract 85.5 from 94 to get 8.5.

$$185.25+8.5^{2}+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Calculate 8.5 to the power of 2 and get 72.25.

$$185.25+72.25+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Add 185.25 and 72.25 to get 257.5.

$$257.5+\left(90-85.5\right)^{2}+\left(87-85.5\right)^{2}$$

Subtract 85.5 from 90 to get 4.5.

$$257.5+4.5^{2}+\left(87-85.5\right)^{2}$$

Calculate 4.5 to the power of 2 and get 20.25.

$$257.5+20.25+\left(87-85.5\right)^{2}$$

Add 257.5 and 20.25 to get 277.75.

$$277.75+\left(87-85.5\right)^{2}$$

Subtract 85.5 from 87 to get 1.5.

$$277.75+1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$277.75+2.25$$

Add 277.75 and 2.25 to get 280.

$$280$$

Factor

$$5\times 7\times 2^{3}$$