First we find the Greatest Common Factor (GFC) for (a + b + c)a and (a + b + c)b.

Greatest Common Factor for (a + b + c)a and (a + b + c)b is (a + b + c).

Then we pull (a + b + c) in front the brackets and what is left in the brackets is a and b:

(a + b + c)a + (a + b + c)b = (a + b + c)(a + b)

In other words the resulting term is a product of the GCF, in our case (a + b + c), and the original expression divided by the GCF:

(a + b + c)a divided by (a + b + c) is a

(a + b + c)b divided by (a + b + c) is b

That is why we have (a + b) in the second brackets.