5.2 Quadratic Expansion with Addition
In chapter 8.6 in the section Operators and Calculation Rules, we covered quadratic multiplication.  Here we split this up into two pages, one for addition and one for subtraction.

We begin with the same example that we covered in chapter 8.6 in Operators and Calculation Rules:

We can also illustrate this in pictures and now see if we will get the same answer:
3
+
7
3
+
7

We count part by part:

3 · 3
+
2(3 · 7)
+
7 · 7  
32
+
2(3 · 7)
  + 72  
9
+
42
  + 49 = 100

We began with 102 which we divided up into two terms, (3 + 7)2, and got that it becomes 32 + 2(3 · 7) + 72 = 100. We now show the calculations.

(3 + 7)2 = 3 + 2(3 · 7) + 7

We try to write the numbers with variables and exchange 3 with a and 7 with b.
With this we have the “general formula” for the rule for addition.  This rule is called the first rule for quadratic expansion.

In some mathematics book then cover quadratic expansion for addition like this:

1. (a + b) = (a + b)(a + b)
4. (a + b)(a + b) = a + ab + ba + b

5. (a + b) = a + 2ab + b

(a + b) = a + 2ab + b (3 + 7) = 3 + 2 · 3 · 7 + 7