# Why (a + b)² = a² + 2ab + b² ?

## Visual Explanation for (a + b)² 🤔

Photo by Shubham Sharan on Unsplash

*(a + b)²**=* ** a² + 2ab + b²,** undoubtedly one of the most famous formulas in mathematics. We were all taught this formula during our childhood

**I knew this formula since the**

*.***age of dinosaurs**(4th standard 😉). But I never knew its mathematical proof till last year. It is not even that complex. It is one of the easiest Mathematical proof I have ever seen. Let us dive into the visual proof.

### Visual Proof 🔥

First, let us consider a Square with length ** a**. What is the area of the square? So simple, it is

*a².*Now, we increase the length of its side by *b**.* Now, the new length will be*a + b**.* The new square will look like …

You can see that, we can divide the new square into 4 shapes

- A square with length
which has an area of*a*.*a²* - 2 Rectangles with length
and breadth*a*which has an area of*b*each.*ab* - A square with length
which has an area of*b*.*b²*

So the area of the new square with length ** a + b** will be

= (Area of the Square with length(a + b)²) + (2 X Area of the Rectangle with lengthaand breadtha) + (Area of the Square with lengthb)b

which can be written as

*(a + b)² = a² + 2ab + b²*

Hence Proved 😎

### Thank you 🤘

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