Algebra: quick ways to solve

Solving math problems quickly: algebra
Do you know what is 5*5? 15*15? Or 25*25?
It gets harder and harder as you increase the numbers before 5. However, I have an easy way to help you get the answer without using a pen or calculator!!
Here is the way:
Please pay a close attention to the pattern:
5*5=25
15*15=225
25*25=625
35*35=1225
45*45=2025
:
What is the pattern? Correct! The results we get all have 25 as the last two digits. So how about the other digits?
Then you should find 1*2=2; 2*3=6; 3*4=12; and so on...
Then the other number should be the number before 5 multiple the same number plus 1.

Using this method, what is 65*65=?
Ans: 4225

What is 11*11=? 121
111*111=? 12321
1111*1111=? 1234321
What is 111111^2=?
Similar method!