1. (2 x 5) + (2 x 3) = 16 FACTORING EXPRESSIONS 5 5 3 3
Factoring is an important process in algebra which is used to simplify expressions, simplify fractions, and solve equations.
Consider the following: Jerry spent $5 for lunch on Monday and again on Tuesday. He spent $3 for snack on each day as well. How much did Jerry spend in all for both days?
2 x x 3
(2 times the cost of lunch) (2 times the cost of snack)
(2 x 5) + (2 x 3) = 16

2. Consider the following: Jerry spent $5 for lunch on Monday and again on Tuesday. He spent $3 for snack on each day as well. How much did Jerry spend in all for both days?
Does the model shown below represent the situation as well?
(cost of lunch and snack (cost of lunch and snack
on Monday) on Tuesday)
2 x (5+ 3) = 16

3. (2 x 5) + (2 x 3) = 2 x (5+ 3) Here’s another view… Let = $1 for lunch
We can look at both expressions to see that they are equivalent.
(2 x 5) + (2 x 3) =
2 x (5+ 3)
Here’s another view…
Let = $1 for lunch
Let = $1 for snack

4. (2 x 5) + (2 x 3) = 2 x (5+ 3) (5 x 3) + (5 x 4) = ___ x ( __ + __)
Mathematically, this equation shows an expression that has been “factored.”
(2 x 5) + (2 x 3) =
2 x (5+ 3)
GCF times THE OTHER SUM
There is a shared factor (GCF) of 2. Take it out and multiply it to the remaining sum.
PRACTICE:
(5 x 3) + (5 x 4) = ___ x ( __ + __)

5. a a b b WRITE AN EXPRESSION REPRESENTING THE TOTAL. _____ _____
_____ _____
The expression that represents the total is ___________

6. Can you rearrange the parts of this bar to represent the total in another way?
Now write a new expression to represent the same total.
a b a b

7. The Distributive Property

8. 3g + 3f = ________________ 6x + 9y = ________________
Use the GCF and the Distributive Property to write equivalent expressions. “Factor.”
3g + 3f = ________________
6x + 9y = ________________
3c + 12c = ________________
24b + 8 = _________________

9. 7x + 7y = _____________________
15g + 20h = ____________________
18m + 42n = _____________________
30a + 39b = ____________________
55m + 11 = ____________________
7 + 56y = ______________________

10. Are these expressions equal? How do you know?
6x + 21y and 3(2x + 7y)

11. Evaluate each expression to prove that these two expressions are equivalent. Let g = 6
5g + 7g g(5 + 7)

12. Evaluate each expression to prove that these two expressions are equivalent. Let x = 10
14x (7x + 1)

13. Fill in the blanks with the numbers that will make the equation true.
4x + 12y = ___ (x + 3y)
35x + ___y = 5 (7x + 10y)
___x + 9y = 9 (2x + y)
32x + 8y = 8 (___x + y)

14. Use models to prove that 3(a + b) = 3a + 3b

15. Use the GCF and the Distributive Property to write equivalent expressions in factored form.
4d + 12e
18x + 30y
21a + 28y

16. Distributing Expressions
The expression 2(a + b) tells us that we have 2 of the
(a + b)’s. Create a tape diagram representing 2 groups of (a + b).
a b a b

17. Show how your model would look if we grouped together the a’s and then grouped together the b’s.
What expression can we write to represent the new diagram?
a a b b

18. Using Area Models to Help Distribute 2 (x + y)

19. Using Area Models to Help Distribute 2 (3x + 4y)

20. Using Area Models to Help Distribute y (4x + 5)

21. Using Area Models to Help Distribute 3 (7d + 4e)