A+number+squared

Today, while grading a test, I noticed something interesting. The answer to a question was 8 squared or 64. But the student wrote 63, which is 7 times 9.

I then noticed that it was the same for 10.

10 squared = 100 9 ∙ 11 = 99

So my hypothesis is:
 * The square of a number is always 1 more than the product of the number one less and the number one more. **

Is this true for all whole numbers? Is it true for all integers?


 * 1 point: ** Email the answer to me by 7:30 am Friday October 28.


 * 4 points: ** Email the answer and an explanation of why or why not to me by 7:30 am Friday October 28.