simple math

I was taught from class 6 that 25 * 25 = (2*3) hundred + 25 and so on

when calculating square of n5 (which is 10n+5) it is (n(n+1))*100+25

I never bothered to know why, but tested it with couple of numbers and said it is working fine.

I was explaining how to calculate squares orally to my wife without using pen and paper. To calculate square of 79, one can calculate it by (80-1)^2


Then i thought I can calculate that of 25 in similar manner.

(10n+5)^2 = (10n)^2+2.10n.5+5^2
=100n^2+100n+25
=100(n^2+n)+25
=n(n+1)100+25