Solve (1000-1)*(1000+1)+(1000-2)*(1000+2)*(1000-3)*(1000+3)=

$$(1000-1) \times (1000+1)+(1000-2) \times (1000+2) \times (1000-3) \times (1000+3)=$$

Evaluate

$$999988000035$$

Solution Steps

Subtract 1 from 1000 to get 999.

$$999\left(1000+1\right)+\left(1000-2\right)\left(1000+2\right)\left(1000-3\right)\left(1000+3\right)$$

Add 1000 and 1 to get 1001.

$$999\times 1001+\left(1000-2\right)\left(1000+2\right)\left(1000-3\right)\left(1000+3\right)$$

Multiply 999 and 1001 to get 999999.

$$999999+\left(1000-2\right)\left(1000+2\right)\left(1000-3\right)\left(1000+3\right)$$

Subtract 2 from 1000 to get 998.

$$999999+998\left(1000+2\right)\left(1000-3\right)\left(1000+3\right)$$

Add 1000 and 2 to get 1002.

$$999999+998\times 1002\left(1000-3\right)\left(1000+3\right)$$

Multiply 998 and 1002 to get 999996.

$$999999+999996\left(1000-3\right)\left(1000+3\right)$$

Subtract 3 from 1000 to get 997.

$$999999+999996\times 997\left(1000+3\right)$$

Multiply 999996 and 997 to get 996996012.

$$999999+996996012\left(1000+3\right)$$

Add 1000 and 3 to get 1003.

$$999999+996996012\times 1003$$

Multiply 996996012 and 1003 to get 999987000036.

$$999999+999987000036$$

Add 999999 and 999987000036 to get 999988000035.

$$999988000035$$

Factor

$$3\times 5\times 199999\times 333331$$