We all know the formula for (a + b)2.

(a + b)2 = a2 + b2+ 2ab

I have observed that when 'a' and 'b' are consecutive numbers, we can use another formula too.

(a + b)2 = 2a2 + 2b2 - 1

You can test using a few examples:

Let's test with 1 and 2

(1 + 2)2 = 2(1)2 + 2(2)2 - 1 = 2 + 2(4) - 1 = 2 + 8 - 1 = 9

Which is the right answer

Let's try it with 6 and 7

( 6 + 7)2 = 2 (6)2 + 2(7)2 - 1

= 2(36) + 2(49) - 1

= 72 + 98 - 1

= 170 - 1

= 169

Which is the right answer

You should try it too.

[ I am Abhiram R from Bangalore. I am studying in Sri Chaitanya Techno Schools in 7th Class C4 Section]