Square of the sum of two terms = square of 1st term + square of 2nd term + 2 × fist term × second term.

    But why??

solution :- Consider a arbitrary line and any arbitrary point on it such that point divides the line       segment  in two parts a & b. 

Then the length of this line is a+b . Now we want to find . so let's make a square of side a+b.

 

  Here, area of square of side a is  and area of square of side b is  . now remaining two rectangle of    side a & b and the Area of rectangle is a*b. therefore the area of two rectangle becomes  2ab. 

  So if we add area of all four parts of big square then we will get area of whole square. i.e

  area of square of side a+b is 

                              

        Hence proved. 

Similarly we can prove,  

                                       

 solution:-          Consider a arbitrary line of length a and take any arbitrary point on it at distance b then  the line divedes in two part as b and a-b .

Now make  square of length a. Then area of this square is sum of all area of all four parts. 

Here area of square of length a-b is and area of square of length b is. also the area of rectangle of side b and a-b is (a-b)*b . so area of such two rectangles becomes 2(a-b)*b.

 Therefore area of big square =
   

                                                 Hence proved.