 Good afternoon. This is Jayati Kodalu from Global Indian International School, Chinchwad. Today we are going to talk about joint people representation of algebraic identity. I am taking the first identity that is A plus B. The whole square is equal to A square plus 2AB plus B square. Now this is the identity we all have. Now we will verify this identity with the help of geometrical figure. But the geometrical figure will help us prove this identity. Now to prove this identity we need a previous knowledge of area of a square. Area of a square everybody knows what it is. Area of a square. Area of a square is nothing but side multiplied by side. Which is nothing but side square. Now we will consider a square whose measurement is A plus B. A plus B is also A plus B. All four sides of the square is nothing but A plus B. Now since this length, this whole length is A plus B. This should be divided in terms of A and B. We will consider this one side a portion of it to be A and the remaining to be B. This is B and this is A. Similarly we will divide this side a portion of this as A and the remaining as B. Same way this side. This portion is A and this portion is B. Here also this is B, this portion this is B and this portion is A. Now this entire geometrical figure is divided into portion. This is portion one, this is portion two, this is three and this is four. Now this area of this entire figure is nothing but area of one portion plus area of two, area of three and plus area of four. Now we will name this area of the, this is the square, this is the square of A plus B units. Now area of the square is equal to A plus B into A plus B. Now one square, this is one, equation one. Now we go to the separate portions. Now we will also, also area of the square is equal to area of one, this one plus area of two plus area of three plus area of four portions. Now this area of one, area of one is nothing but, it's also for bigger square. This is A units, this is A units and this is A units and this also is A unit. So area of one is a square, area of one is nothing but A into A plus area of portion two. It's a rectangle, can you see this is a rectangle, this shape is, this shape is a rectangle. The area of this rectangle is length into breadth, that is A into B, A into B plus area of whole portion. Area of third portion is also a rectangle, that is B into A or A into B is the same. So this is again A into B plus area of the fourth portion, this fourth portion forms a square. Can you see this, this fourth one is also a square of B units, B units. So that is B square. So this will be nothing but A square plus A B plus A B plus, this will be nothing but A square plus two A B plus B square. Now in this equation, area of the square in this equation, we substitute the value of this. In this, now the area of the square we have generated from one is A plus B, the whole square. This side, area of the square is this one, which is equal to the area of the square which is equal to two. That is A square plus two A B plus B square. This is how we prove the joint become identity A plus B, the whole square is equal to A square plus two A B plus B square.