Solve =(1000)^3-(2)^3-3*(1000)^2*2+3*1000*(2)^2

$$= ( 1000 ) ^ { 3 } - ( 2 ) ^ { 3 } - 3 \times ( 1000 ) ^ { 2 } \times 2 + 3 \times 1000 \times ( 2 ) ^ { 2 }$$

Evaluate

$$994011992$$

Solution Steps

Calculate 1000 to the power of 3 and get 1000000000.

$$1000000000-2^{3}-3\times 1000^{2}\times 2+3\times 1000\times 2^{2}$$

Calculate 2 to the power of 3 and get 8.

$$1000000000-8-3\times 1000^{2}\times 2+3\times 1000\times 2^{2}$$

Subtract 8 from 1000000000 to get 999999992.

$$999999992-3\times 1000^{2}\times 2+3\times 1000\times 2^{2}$$

Calculate 1000 to the power of 2 and get 1000000.

$$999999992-3\times 1000000\times 2+3\times 1000\times 2^{2}$$

Multiply 3 and 1000000 to get 3000000.

$$999999992-3000000\times 2+3\times 1000\times 2^{2}$$

Multiply 3000000 and 2 to get 6000000.

$$999999992-6000000+3\times 1000\times 2^{2}$$

Subtract 6000000 from 999999992 to get 993999992.

$$993999992+3\times 1000\times 2^{2}$$

Multiply 3 and 1000 to get 3000.

$$993999992+3000\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$993999992+3000\times 4$$

Multiply 3000 and 4 to get 12000.

$$993999992+12000$$

Add 993999992 and 12000 to get 994011992.

$$994011992$$

Factor

$$2^{3}\times 499^{3}$$