SOLUTION: Geometricly prove that: (x+y)^2 = x^2+2xy+y^2 (x-y)^2 = x^2-2xy+y^2 (x+y)(x-y) = x^2-y^2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Geometricly prove that: (x+y)^2 = x^2+2xy+y^2 (x-y)^2 = x^2-2xy+y^2 (x+y)(x-y) = x^2-y^2      Log On


   

Question 28727: Geometricly prove that:
(x+y)^2 = x^2+2xy+y^2
(x-y)^2 = x^2-2xy+y^2
(x+y)(x-y) = x^2-y^2
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
I SHALL SHOW YOU THE FIRST ..TRY DOING OTHERS IN A SIMILAR WAY.IF IN DIFFICULTY COME BACK.
DRAW A RECTANGLE HAVING ABC AS THE BOTTOM SIDE WITH AB=X AND BC=Y..SO THAT ABC=AB+BC=X+Y
DRAW CDE AS ITS ADJACENT SIDE AT RIGHT ANGLES WITH BC=CD=Y AND DE=X...SO THAT
CDE = CD+DE=Y+X
COMPLETE THE RECTANGLE IN THE SAME WAY DRAWING EFG AS TOP SIDE WITH EF=Y AND FG=X
DRAW GHA SO THAT GH =X AND HA=Y
JOIN BF AND DH.LET THEM MEET AT K
SO AREA OF RECTANGLE ABCDEFGH = (X+Y)(X+Y)=(X+Y)^2=
=AREA OF RECTANGLE ABKH +AREA OF RECTANGLE BCDK+AREA OF RECTANGLE DEFK +AREA OF RECTANGLE FGHK
=XY+Y^2+XY+X^2=X^2+Y^2+2XY