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.
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