You can make a model to prove the identity .(a + b)² This is easy. On a piece of paper, make a square of length (a + b) [Choose a and b as per your wish t be any two lengths].Its area represents (a + b)². Make another square of side a, and another of side b.
Make a rectangle of side 2a and b or 2b and a, whichever is convenient.
Put the side a square, side b square and the rectangle on the bigger square of side (a + b). You can show that this fits perfectly, thus proving the identity.