Solve frac{79^{3}+21^{3}}{79^2-79*21+21^2}-66^2-34^2/100

$$\frac { 79 ^ { 3 } + 21 ^ { 3 } } { 79 ^ { 2 } - 79 \cdot 21 + 21 ^ { 2 } } - \frac { 66 ^ { 2 } - 34 ^ { 2 } } { 100 }$$

Evaluate

$$68$$

Solution Steps

Calculate 79 to the power of 3 and get 493039.

$$\frac{493039+21^{3}}{79^{2}-79\times 21+21^{2}}-\frac{66^{2}-34^{2}}{100}$$

Calculate 21 to the power of 3 and get 9261.

$$\frac{493039+9261}{79^{2}-79\times 21+21^{2}}-\frac{66^{2}-34^{2}}{100}$$

Add 493039 and 9261 to get 502300.

$$\frac{502300}{79^{2}-79\times 21+21^{2}}-\frac{66^{2}-34^{2}}{100}$$

Calculate 79 to the power of 2 and get 6241.

$$\frac{502300}{6241-79\times 21+21^{2}}-\frac{66^{2}-34^{2}}{100}$$

Multiply 79 and 21 to get 1659.

$$\frac{502300}{6241-1659+21^{2}}-\frac{66^{2}-34^{2}}{100}$$

Subtract 1659 from 6241 to get 4582.

$$\frac{502300}{4582+21^{2}}-\frac{66^{2}-34^{2}}{100}$$

Calculate 21 to the power of 2 and get 441.

$$\frac{502300}{4582+441}-\frac{66^{2}-34^{2}}{100}$$

Add 4582 and 441 to get 5023.

$$\frac{502300}{5023}-\frac{66^{2}-34^{2}}{100}$$

Divide 502300 by 5023 to get 100.

$$100-\frac{66^{2}-34^{2}}{100}$$

Calculate 66 to the power of 2 and get 4356.

$$100-\frac{4356-34^{2}}{100}$$

Calculate 34 to the power of 2 and get 1156.

$$100-\frac{4356-1156}{100}$$

Subtract 1156 from 4356 to get 3200.

$$100-\frac{3200}{100}$$

Divide 3200 by 100 to get 32.

$$100-32$$

Subtract 32 from 100 to get 68.

$$68$$

Factor

$$2^{2}\times 17$$