Solve (783+517)*(783^2-783*517+517^2)/783^2-2*783*517+517^2+783*517

$$\frac{ (783+517) \times ( { 783 }^{ 2 } -783 \times 517+ { 517 }^{ 2 } ) }{ { 783 }^{ 2 } -2 \times 783 \times 517+ { 517 }^{ 2 } +783 \times 517 }$$

Evaluate

$$1300$$

Solution Steps

Add 783 and 517 to get 1300.

$$\frac{1300\left(783^{2}-783\times 517+517^{2}\right)}{783^{2}-2\times 783\times 517+517^{2}+783\times 517}$$

Calculate 783 to the power of 2 and get 613089.

$$\frac{1300\left(613089-783\times 517+517^{2}\right)}{783^{2}-2\times 783\times 517+517^{2}+783\times 517}$$

Multiply 783 and 517 to get 404811.

$$\frac{1300\left(613089-404811+517^{2}\right)}{783^{2}-2\times 783\times 517+517^{2}+783\times 517}$$

Subtract 404811 from 613089 to get 208278.

$$\frac{1300\left(208278+517^{2}\right)}{783^{2}-2\times 783\times 517+517^{2}+783\times 517}$$

Calculate 517 to the power of 2 and get 267289.

$$\frac{1300\left(208278+267289\right)}{783^{2}-2\times 783\times 517+517^{2}+783\times 517}$$

Add 208278 and 267289 to get 475567.

$$\frac{1300\times 475567}{783^{2}-2\times 783\times 517+517^{2}+783\times 517}$$

Multiply 1300 and 475567 to get 618237100.

$$\frac{618237100}{783^{2}-2\times 783\times 517+517^{2}+783\times 517}$$

Calculate 783 to the power of 2 and get 613089.

$$\frac{618237100}{613089-2\times 783\times 517+517^{2}+783\times 517}$$

Multiply 2 and 783 to get 1566.

$$\frac{618237100}{613089-1566\times 517+517^{2}+783\times 517}$$

Multiply 1566 and 517 to get 809622.

$$\frac{618237100}{613089-809622+517^{2}+783\times 517}$$

Subtract 809622 from 613089 to get -196533.

$$\frac{618237100}{-196533+517^{2}+783\times 517}$$

Calculate 517 to the power of 2 and get 267289.

$$\frac{618237100}{-196533+267289+783\times 517}$$

Add -196533 and 267289 to get 70756.

$$\frac{618237100}{70756+783\times 517}$$

Multiply 783 and 517 to get 404811.

$$\frac{618237100}{70756+404811}$$

Add 70756 and 404811 to get 475567.

$$\frac{618237100}{475567}$$

Divide 618237100 by 475567 to get 1300.

$$1300$$

Factor

$$2^{2}\times 5^{2}\times 13$$