(a+b)2 = a2 + b2 + 2ab: This is how mathematics should be taught

@Ramani Aswath • 08 Dec, 2012 The Maharashtrian mathematecian Bhaskara II gave an interesting algebraic proof of the pythagorean Theorem:
Proof #4

The fourth approach starts with the same four triangles, except that, this time, they combine to form a square with the side (a + b) and a hole with the side c. We can compute the area of the big square in two ways. Thus
(a + b)² = 4·ab/2 + c²
simplifying which we get the needed identity.
A proof which combines this with proof #3 is credited to the 12th century Hindu mathematician Bhaskara (Bhaskara II):

Here we add the two identities
c² = (a - b)² + 4·ab/2 and
c² = (a + b)² - 4·ab/2
which gives
2c² = 2a² + 2b².
The latter needs only be divided by 2.

https://www.cut-the-knot.org/pythagoras/index.shtml

TEachers must make it interesting to students.