Solve (200^2*201^2-100^2*101^2)/4

$$( 200 ^ { 2 } \cdot 201 ^ { 2 } - 100 ^ { 2 } \cdot 101 ^ { 2 } ) / 4$$

Evaluate

$$378507500$$

Solution Steps

Calculate 200 to the power of 2 and get 40000.

$$\frac{40000\times 201^{2}-100^{2}\times 101^{2}}{4}$$

Calculate 201 to the power of 2 and get 40401.

$$\frac{40000\times 40401-100^{2}\times 101^{2}}{4}$$

Multiply 40000 and 40401 to get 1616040000.

$$\frac{1616040000-100^{2}\times 101^{2}}{4}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{1616040000-10000\times 101^{2}}{4}$$

Calculate 101 to the power of 2 and get 10201.

$$\frac{1616040000-10000\times 10201}{4}$$

Multiply 10000 and 10201 to get 102010000.

$$\frac{1616040000-102010000}{4}$$

Subtract 102010000 from 1616040000 to get 1514030000.

$$\frac{1514030000}{4}$$

Divide 1514030000 by 4 to get 378507500.

$$378507500$$

Factor

$$2^{2}\times 5^{4}\times 7\times 43\times 503$$