Objective- To use the distributive property to simplify variable expressions.

1
Objective- To 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(3) 6(5)
6(8)
48
18 30
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
12 4r
8
3) 7(8 m)
8) 2(x 8)
2x 16
56
7m
4) 3(4 a)
9) 7(2m 3y 4)
12
14m 21y 28
3a
5) (3 k)5
10) (6 2y a)3
15
18 6y 3a
5k
3
Use the distributive property to simplify.
1) 4(y 7)
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 3 t)
20 5a
10m 15 5t
5) (7 k)6
10) (11 2y)3y
42 6k
11 5y
4
Geometric Model for Distributive Property
3 7
4
Two ways to find the total area.
Width by total length
Sum of smaller rectangles
4(3 7)
5
Geometric Model for Distributive Property
3 7
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
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
9
Factoring
One type involves the Distributive Property in
reverse.
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.
Unlike Terms
Like Terms
7x 3y
7x 3x
5y y
5y
10xy 2yx
2a 3ab
12
Simplify by combining like terms.
1) 7x 4y 2x y
5) 4k (2j) 6k j
3j
10k
9x
5y
2) 3m 10n 4m 1
6) 10 4x 3y 17x
21x
7m
10n
1
3y
10
7)
3) 7x 3y
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 28 2x
3b 6 6b
9x
28
9b
6
6) 5x 3(x 1)
9) 2(3m 1) 4m
5x 3x 3
6m 2 4m
8x
3
10m
2
7) a 2(4 a ) 1
10) 3(k m) 5(k 2m)
5k 10m
a 8 2a 1
3k 3m
3a
9
8k
13m