1.5 The Distributive Property

• Notice that it does not matter whether a is placed on the right or the left of the expression in the parentheses.

• The Symmetric Property of Equality allows the Distributive Property to be written as follows.

• If a(b + c) = ab + ac, then ab + ac = a(b + c).

Distribute Over Addition

• Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.

8(10 + 4)= 8(10) + 8(4)= 80 + 32= 112

Distribute Over Subtraction

• Rewrite (12 - 3)6 using the Distributive Property. Then evaluate.

(12 – 3)6= 12(6) – 3(6)= 72 – 18= 54

Use the Distributive Property• The Morris family owns two cars. In 1998, they drove the

first car 18,000 miles and the second car 16,000 miles. Use the graph to find the total cost of operating both cars.

Use the Distributive Property

• Use the Distributive Property to write and evaluate an expression.0.46(18,000 + 16,000)

= 8280 + 7360= 15,640

It cost the Morris family $15,640 to operate their cars.

Use the Distributive Property• Use the Distributive Property to find the product.a. 15 · 99

= 15 (100 – 1)= 15(100) – 15(1)= 1500 – 15= 1485

Use the Distributive Property• Use the Distributive Property to find the product.

1.35 25

b

135 25

135 2 355

70 7

77

Algebraic Expressions• Rewrite each product using the Distributive

Property. Then simplify.a. 5(g – 9)

= 5g – 45

b.3(2x² + 4x – 1)= 3(2x²) + 3(4x) – 3(1)= 6x² + 12x – 3

Combine Like Terms• A term is a number, a variable, or a product or

quotient of numbers and variables.• Like terms are terms that contain the same

variables, with corresponding variables having the same power.

• The expressions 5n + 7n and 12n are called equivalent expressions because they denote the same number.

• An expression is in simplest form when it is replaced by an equivalent expression having no like terms or parentheses.

Combine Like Terms

• Simplify each expression.a. 15x + 18x

= (15 + 18)x= 33x

b.10n + 3n² + 9n²= 10n + (3 + 9)n²= 10n + 12n²

Coefficient

• The coefficient of a term is the numerical factory. – For example, in 17xy, the coefficient is 17.