Solve (832-300)^2*2+(832-500)^2*8+(832-700)^2*30+(832-900)^2*42

$$( 832 - 300 ) ^ { 2 } \times 2 + ( 832 - 500 ) ^ { 2 } \times 8 + ( 832 - 700 ) ^ { 2 } \times 30 + ( 832 - 900 ) ^ { 2 } \times 42$$

Evaluate

$$2164768$$

Solution Steps

Subtract 300 from 832 to get 532.

$$532^{2}\times 2+\left(832-500\right)^{2}\times 8+\left(832-700\right)^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Calculate 532 to the power of 2 and get 283024.

$$283024\times 2+\left(832-500\right)^{2}\times 8+\left(832-700\right)^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Multiply 283024 and 2 to get 566048.

$$566048+\left(832-500\right)^{2}\times 8+\left(832-700\right)^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Subtract 500 from 832 to get 332.

$$566048+332^{2}\times 8+\left(832-700\right)^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Calculate 332 to the power of 2 and get 110224.

$$566048+110224\times 8+\left(832-700\right)^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Multiply 110224 and 8 to get 881792.

$$566048+881792+\left(832-700\right)^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Add 566048 and 881792 to get 1447840.

$$1447840+\left(832-700\right)^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Subtract 700 from 832 to get 132.

$$1447840+132^{2}\times 30+\left(832-900\right)^{2}\times 42$$

Calculate 132 to the power of 2 and get 17424.

$$1447840+17424\times 30+\left(832-900\right)^{2}\times 42$$

Multiply 17424 and 30 to get 522720.

$$1447840+522720+\left(832-900\right)^{2}\times 42$$

Add 1447840 and 522720 to get 1970560.

$$1970560+\left(832-900\right)^{2}\times 42$$

Subtract 900 from 832 to get -68.

$$1970560+\left(-68\right)^{2}\times 42$$

Calculate -68 to the power of 2 and get 4624.

$$1970560+4624\times 42$$

Multiply 4624 and 42 to get 194208.

$$1970560+194208$$

Add 1970560 and 194208 to get 2164768.

$$2164768$$

Factor

$$2^{5}\times 61\times 1109$$