In today’s post we will look at how to calculate the square of the sum of two numbers a and b, (a + b) ².

### Notable Identities:

For example: We built a square with sides of **a + b** units length:

If we calculate the area of this square (we know that the area of a square is side multiplied by side), it gives us: (a + b)(a + b), which would be the same as **(a + b) ²** square units.

Then we will divide the square into four parts:

Now, we have two squares (blue and red) and two rectangles (green and yellow). We calculate the areas of each figure:

It is easy to see that the area of the first pink square of side a + b, is the sum of the areas of the blue square (= a²), of the red (= b ²) and the two equal yellow and green rectangles (= 2ab)

Therefore, we can see that **(a + b) ² = a² + 2ab + b ².**

There are several **identities of great importance in mathematics** that must be learned to be handled with ease:

(a+b) ² = a² + 2ab + b ²

(a-b) ² = a² – 2ab + b ²

(a+b)(a-b) = a² – b²

Often they lead us to make mistakes when doing calculations with them, so it is important not to simply memorize formulas but *try to see where they come from.*

We have just seen, from the geometric point of view, how to square the sum of two quantities (in our case a and b).

I hope you liked this post and that it has helped you understand the notable identities a little more. We can do the same with squaring the difference of the two numbers and multiplying the sum by the difference. Try to do it yourself, I am sure it will come out well!

Remember that at Smartick you can practice identity exercises, and much more!

Learn More:

- Distributive Property in Geometry
- How to Perform Multiplication Problems with an Area Model
- Learn about the Distributive Property of Multiplication
- Calculating the Area of Polygons
- Let’s Learn about Ratios with Singaporean Bar Models