(a+b)^2=a^2+2ab+b^2 But why?

So Lets prove it :
Consider a line 

Take any arbitrary point 

So now we can say that length of line is a+b
Now we have to square a+b
that will be

lets add all the squares and rectangles

This will be  a² 

Now it is a²+b²

Here there are two rectangle in the above diagram

As we know that Area of rectangle is Length X Width

So it will be a x b

Now lets add every square and rectangle

a² + b² + a x b + a x bi.e., a² + b² + 2ab

Thus 

(a+b)²=a² + 2ab+b² 

Posted in: Formulas, Geometry, Interesting Tricks, Maths, Squaring