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

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

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

(a + b)² = (Area of the Square with length a) + (2 X Area of the Rectangle with length a and breadth b) + (Area of the Square with length b)

which can be written as

(a + b)² = a² + 2ab + b²

Hence Proved 😎

Thank you 🤘

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