1. Common Core Standard 7.EE.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Student Objective: Use the distributive property to simplify variable expressions.
Distributive Property
a(b + c) = ab + ac
Order of Operations
Distributive Property
6(3 + 5)
6(3 + 5)
6(8)
6(3) + 6(5) 48 48

3. Use the distributive property to simplify.
1) 3(x + 7)
6) x(a + m)
ax + mx 3x
+ 21
2) 2(a + 4)
7) 4(3 + r) 2a
+ 8
12 + 4r
3) 7(8 + m)
8) 2(x + 8)
2x + 16 56
+ 7m
4) 3(4 + a)
9) 7(2m + 3y + 4) 12
+ 3a
14m + 21y + 28
5) (3 + k)5
10) (6 + 2y + a)3 15
+ 5k
18 + 6y + 3a

4. Use the distributive property to simplify.
6) a(c + d)
4y + 28
ac + ad
2) 3(b + 6)
7) 8(3 + r)
3b + 18
24 + 8r
3) 5(9 + m)
8) 4(x + y + 1)
45 + 5m
4x + 4y + 4
4) 5(4 + a)
9) 5(2m t)
20 + 5a
10m t
5) (7 + k)6
10) (11 + 2y)+3y
42 + 6k
11 + 5y

5. 4(3 + 7) Geometric Model for Distributive Property 3 7 4 4
Two ways to find the total area.
Width by total length
Sum of smaller rectangles
4(3 + 7)

6. = 4(3 + 7) 4(3) + 4(7) Geometric Model for Distributive Property 3 7 4 4
4(3)
4(7)
Two ways to find the total area.
Width by total length
Sum of smaller rectangles =
4(3 + 7)
4(3) + 4(7)
4(10) 12 + 28 40 40

7. = 9(4 + x) 9(4) + 9(x) Geometric Model for Distributive Property 4 x 9
Two ways to find the total area.
Width by total length
Sum of smaller rectangles =
9(4 + x)
9(4) + 9(x)

8. Does Order of Operations
Geometric Model for Distributive Property x 9
9(4)
9(x)
Two ways to find the total area.
Width by total length
Sum of smaller rectangles =
9(4 + x)
9(4) + 9(x) 36 + 9x
Does Order of Operations
help to simplify here?

9. Factoring
Find the missing factor. 1) 2) 3) 4) 5)

10. GCF: GCF: GCF: GCF: Factoring GCF - Greatest Common Factor
Find the GCF of the following mentally. 1) 2) 3) 4)
GCF:
GCF:
GCF:
GCF:

11. GCF: ___ 2 GCF: ___ 5 GCF: ___ 7 GCF: ___ 4 Factoring
One type involves the Distributive Property in
reverse.
Factor the following expression. FIND GCF first: 1) 2) 3) 4)
GCF: ___ 2
GCF: ___ 5
GCF: ___ 7
GCF: ___ 4

12. Factoring
One type involves the Distributive Property in
reverse.
Factor the following expression. 5) 7) 6) 8)

13. Like Terms Like Terms Unlike Terms 7x 3x 7x 3y 5y y 5y 10xy 2yx 2a 3ab
Variable terms that differ only in their coefficients.
Variables must be same letters and powers (exponents).
Ex) x can only combine with other x terms. x can only combine with other x terms. 2 2
Like Terms
Unlike Terms
7x x
7x y
5y y 5y
10xy yx
2a ab

14. Simplify by combining like terms.
1) 7x + 4y + 2x + y
5) 4k + (2j) + 6k + j 9x
+ 5y
10k
+ 3j
2) 3m + 10n + 4m + 1
6) x + 3y + 17x 7m
+ 10n
+ 1
21x
+ 3y
+ 10
3) 7x + 3y 7)
7x + 3y
4) 6x + (5x) + 2x + 3 8)
13x
+ 3

15. Simplify the expression using the Distributive
Property and then combining like terms. 1) 3) 2) 4)

16. Simplify each variable expression.
5) 7(x + 4) + 2x
8) 3(b + 2) + 6b
7x x
3b b 9x
+ 28 9b
+ 6
6) 5x + 3(x + 1)
9) 2(3m + 1) + 4m
5x + 3x + 3
6m m 8x
+ 3
10m
+ 2
7) a + 2(4 + a ) + 1
10) 3(k + m) + 5(k + 2m)
a a + 1
3k + 3m
+ 5k + 10m 3a
+ 9 8k
+ 13m