Solve 8*(25*26/2)^2-8(10*11/2)^2

$$8 \times ( \frac { 25 \times 26 } { 2 } ) ^ { 2 } - 8 ( \frac { 10 \times 11 } { 2 } ) ^ { 2 }$$

Evaluate

$$820800$$

Solution Steps

Multiply 25 and 26 to get 650.

$$8\times \left(\frac{650}{2}\right)^{2}-8\times \left(\frac{10\times 11}{2}\right)^{2}$$

Divide 650 by 2 to get 325.

$$8\times 325^{2}-8\times \left(\frac{10\times 11}{2}\right)^{2}$$

Calculate 325 to the power of 2 and get 105625.

$$8\times 105625-8\times \left(\frac{10\times 11}{2}\right)^{2}$$

Multiply 8 and 105625 to get 845000.

$$845000-8\times \left(\frac{10\times 11}{2}\right)^{2}$$

Multiply 10 and 11 to get 110.

$$845000-8\times \left(\frac{110}{2}\right)^{2}$$

Divide 110 by 2 to get 55.

$$845000-8\times 55^{2}$$

Calculate 55 to the power of 2 and get 3025.

$$845000-8\times 3025$$

Multiply 8 and 3025 to get 24200.

$$845000-24200$$

Subtract 24200 from 845000 to get 820800.

$$820800$$

Factor

$$2^{6}\times 3^{3}\times 5^{2}\times 19$$