1. GCF other factor of 36 other factor of 42
Factoring Sums
When we factor expressions, we are being asked to rewrite the expression with the GCF. We are not being asked to evaluate (solve) the expression.
Example:
= 6 x (6 + 7)
GCF other factor of other factor of 42
of 36 and 42

2. Let’s take a closer look!
= 6 x (6 + 7)
Here are 36 and 42 “things.”

3. Let’s take a closer look!
= 6 x (6 + 7)
Here are 36 and 42 “things.”
We can divide these 42 “things” into groups of 2 or 3 or 6 evenly. Since 6 is the greatest number of groups, then we will show division using 6.

4. 6 Groups Let’s take a closer look! 36 + 42 = 6 x (6 + 7)
Here are 36 and 42 “things.”
6 Groups

5. 6 Groups Let’s take a closer look! 36 + 42 = 6 x (6 + 7)
Here are 36 and 42 “things.”
6 Groups
6 in each group here 7 in each group here

6. 6 Groups Let’s take a closer look! 36 + 42 = 6 x (6 + 7)
Here are 36 and 42 “things.”
6 Groups
6 in each group here 7 in each group here
So can be written as 6 groups of 6 and 7…

7. = 6 x (6 + 7)
Using the distributive property of mathematics, we can check our answer.
6 x (6 + 7)
Take the GCF of 6 and multiply it to each addend. You should get the expression that was first given to you,

8. Here are some other examples of expressions that were factored completely using the GCF and the distributive property.
= 6(2 + 3) (2 + 3) =
= 8(5 + 9) (5 + 9) =
= 4(25 + 9) (25 + 9) =
And here is the check using the distributive property

9. You Try!
= ___ ( ___ + ___)
= ___ ( ___ + ___)
= ___ ( ___ + ___)
= ___ ( ___ + ___)
Hmmm??
x(y) + x(z) = ___ ( ___ + ___)