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Now lets try to understand this method using algebra.

We know that we can express any 2 digit number as 10m+n , where m is the digit at tens place and n is the digit at ones place.

Now we have to find its square, i.e. (10m + n)²

(10m + n)² = (10m)² + 2× 10m× n + n² ……….using, (x+y)² = x² + 2xy + y²

=( m² × 100) + ( 2mn× 10 )+ (n² )

Now, carefully observe the above method, you will see that we were finding these terms only and then addition of these terms gives us the required square.