1. Objective- To use the distributive property to simplify variable expressions.
a(b + c) = ab + ac
Order of Operations
Distributive Property
6(3 + 5)
6(3 + 5)
6(8)
6(3) + 6(5) 48 48
Why distribute when order of operations is faster ?

2. 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

3. 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

4. 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)

5. = 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)

6. = 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)

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

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

9. Factoring
One type involves the Distributive Property in
reverse.
Factor the following expression. 1) 2) 3) 4)

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

11. Like Terms
Like terms - variable terms that differ only in
their coefficients.
Like Terms
Unlike Terms
7x x
7x y
5y y 5y
10xy yx
2a ab

12. 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

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

14. 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