1. 1-5 The distributive Property
You can use algebra tiles to model algebraic expressions. 1
1-tile 1
x-tile 1 x
This 1-by-1 square tile has an area of 1 square unit.
This 1-by-x square tile has an area of x square units.
Model the Distributive Property using Algebra Tiles 3 3 x 3 2
x + 2 +
x + 2
Area = 3(x + 2)
Area = 3(x ) + 3(2)

2. a(b + c) = ab + ac 2(x + 5) = 2(x) + 2(5) = 2x + 10 (b + c)a = ba + ca
USE THE DISTRIBUTIVE PROPERTY
THE DISTRIBUTIVE PROPERTY
The product of a and (b + c):
a(b + c) = ab + ac
2(x + 5) =
2(x) + 2(5) =
2x + 10
(b + c)a = ba + ca
(x + 5)2 =
(x)2 + (5)2 =
2x + 10
y(1 – y) =
y(1) – y(y) =
y – y 2 = =
(1 + 5x)2
(1)2 + (5x)2
2 + 10x

3. (–3)(1 + x) = (–3)(1) + (–3)(x) = –3 – 3x (y – 5)(–2)
USING THE DISTRIBUTIVE PROPERTY
Remember that a factor must multiply each term of an expression.
(–3)(1 + x)
= (–3)(1) + (–3)(x)
Distribute the –3.
Simplify.
= –3 – 3x
(y – 5)(–2)
= (y)(–2) + (–5)(–2)
Distribute the –2.
Simplify.
= –2y + 10
–(7 – 3x)
= (–1)(7) + (–1)(–3x)
–a = –1 • a
Simplify.
= –7 + 3x
Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

4. You are shopping for CDs. You want to buy six CDs for $11.95 each.
MENTAL MATH CALCULATIONS
SOLUTION
You are shopping for CDs.
You want to buy six CDs
for $11.95 each.
The mental math is easier if you think of $11.95 as $12.00 – $.05.
6(11.95) = 6(12 – 0.05)
Write as a difference.
= 6(12) – 6(0.05)
Use the distributive property
to calculate the total cost
mentally.
Use the distributive property.
= 72 – 0.30
Find the products mentally.
= 71.70
Find the difference mentally.
The total cost of 6 CDs at $11.95 each is $71.70.

5. x is the y is the x2 y3 y2 – x2 + 3y3 – 5 + 3 – 3x2 + 4y3 + y + – 3 y2
SIMPLIFYING BY COMBINING LIKE TERMS
Each of these terms is the product of a number and a variable.
Each of these terms is the product of a number and a variable.
terms + – 3 y2 x
variable. + – 3 y2 x
number + – 3 y2 x + – 3 y2 x
x is the
variable.
y is the
–1 is the
coefficient of x.
3 is the
coefficient of y2.
variable
power.
Like terms
Like terms have the same variable raised to the same power.
y2 – x2 + 3y3 – – 3x2 + 4y3 + y
The constant terms –5 and 3 are also like terms. x2 y3

6. 8x + 3x = (8 + 3)x = 11x 4x2 + 2 – x2 = 4x2 – x2 + 2 = 3x2 + 2
SIMPLIFYING BY COMBINING LIKE TERMS
8x + 3x =
(8 + 3)x
Use the distributive property.
= 11x
Add coefficients.
4x2 + 2 – x2 =
4x2 – x2 + 2
Group like terms.
= 3x2 + 2
Combine like terms.
3 – 2(4 + x) =
3 + (–2)(4 + x)
Rewrite as addition expression.
= 3 + [(–2)(4) + (–2)(x)]
Distribute the –2.
= 3 + (–8) + (–2x)
Multiply.
= –5 + (–2x)
Combine like terms
and simplify.
= –5 – 2x