Question

evaluate 1003square-997square​

Answer 1

Answer:

The answer is "12000".

Solution:

Since

1003 = 1000 + 3

 977 = 1000 - 3

So

1003² = (1000 + 3)²

 977² = (1000 - 3)²

Using formulas

(a + b)² = a² + 2(a)(b) + b²

(a - b)² = a² - 2(a)(b) + b²

we get

1003² - 997² =  (1000 + 3)² - (1000 - 3)²

                      =  (1000000 + 2(1000)(3) + 9) -  (1000000 - 2(1000)(3) + 9)

                      = 6000 + 6000 = 12000

So

The answer is "12000".

Answer 2

Answer:

$1003^2-997^2=12000$

Step-by-step explanation:

Formula used:

$a^2-b^2=(a+b)(a-b)$

$1003^2-997^2$

$=(1000+3)^2-(1000-3)^2$

$=(1000+3+1000-3)(1000+3-(1000-3))$

$=(1000+3+1000-3)(1000+3-1000+3)$

$=(1000+1000)(3+3)$

$=(2000)(6)$

$=12000$