4GMAT - Online GMAT Preparation

Hello,

I have just started to work on the 4gmat books and I have a problem to understand the answer of the question 34 under the Number Properties section.

Question:
1000*1000 - 999 * 999 = ?

I solved it this way:
10^6 - (1000-1) ^2 = 10^6 - (10^6 -2000 +1) = 1999

However, the book just mentions:
(1000+99) * (1000-999) = 1999

Can someone please explain the book's process or rule it is using ?

Thanks.

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

1000*1000 - 999 * 999 = 1000^2 - 999^2 = (1000+999) (1000-999) = 1999*1 = 1999