(25)^2= (2*3 25)=625

(35)^2 =(3*4 25)=1225

(45)^2=(4*5 25)=2025

Let "10x + 5" be represented as [x][5]. Ex. 25 as [2][5].

.

Now,

[x][5] * [x][5]

= [x*(x+1)] [2] [5]

.

.

This applies to any 2 numbers satisfying following conditions:

Ist Number: [a] [b]

IInd Number: [a] [c]

Conditions:

1. As you can note, the left digit should be same in bothe numbers, i.e. [a], here.

2. 'b' + 'c' = 10

.

Then,

[a] [b] * [a] [c]

= [a*(a+1)] [b*c]

.

Example:

23*27

= [2*(2+1)] [3*7]

= [2*3] [21]

= [6] [2] [1]

= 621