Download Algebraic Expressions and Models

1.2
Algebraic Expressions
and Models
Goals p Evaluate algebraic expressions.
p Simplify algebraic expressions.
Your Notes
VOCABULARY
Numerical expression An expression that consists of
numbers, operations, and grouping symbols
Base of a power The number in a power used as a
factor
Exponent The number in a power that represents the
number of times the base is used as a factor
Power An expression such as 25, which represents
2 p 2 p 2 p 2 p 2 ⫽ 32
Variable A letter used to represent one or more
numbers
Algebraic expression An expression involving variables
Mathematical model A mathematical representation of
a real-life situation
Terms of an expression The parts of an algebraic
expression that are added together
Coefficient When a term is the product of a number
and a power of a variable, the number is the
coefficient of the power
Like terms Terms that have the same variable part
Constant term A term that has no variable part
Equivalent algebraic expressions Expressions that have
the same value for all values of their variable(s)
Identity A statement that equates two equivalent
expressions
4
Algebra 2 Notetaking Guide • Chapter 1
Your Notes
Example 1
Evaluating Powers
a. (⫺2)4 ⫽ (⫺2) p (⫺2) p (⫺2) p (⫺2) ⫽ 16
b. ⫺24 ⫽ ⫺(2 p 2 p 2 p 2) ⫽ ⫺16
ORDER OF OPERATIONS
1. First, do operations that occur within grouping symbols .
2. Next, evaluate powers .
3. Then, do multiplications and divisions from left to right .
4. Finally, do additions and subtractions from left to right .
Example 2
Using Order of Operations
3 ⫹ 4(8 ⫺ 6)2 ⫽ 3 ⫹ 4( 2 )2
Example 3
Add within parentheses.
⫽ 3 ⫹ 4( 4 )
Evaluate power.
⫽ 3 ⫹ 16
Multiply.
⫽ 19
Add.
Evaluating an Algebraic Expression
Evaluate 2x2 ⴚ 6x ⴚ 3 when x ⴝ 3.
2x2 ⫺ 6x ⫺ 3 ⫽ 2( 3 )2 ⫺ 6( 3 ) ⫺ 3
Substitute for x.
⫽ 2( 9 ) ⫺ 6( 3 ) ⫺ 3
Evaluate power.
⫽ 18 ⫺ 18 ⫺ 3
Multiply.
⫽ ⫺3
Add.
Checkpoint Complete the following exercises.
1. Evaluate 7 ⫹ 8(⫺2 ⫹ 4)2.
39
2. Evaluate ⫺4x2 ⫹ 2x ⫹ 9
when x ⫽ 2.
⫺3
Lesson 1.2 • Algebra 2 Notetaking Guide
5
Your Notes
Writing and Evaluating a Real-Life Model
Example 4
You have $40 and are buying books that cost $12 each.
Write an expression that shows how much money you have
left after buying n books. Evaluate the expression when
n ⫽ 1 and n ⫽ 3.
Solution
Verbal
Model
Labels
Original
amount
⫺
Price per
book
p
Number of
books bought
Original amount ⫽ 40
(dollars)
Price per book ⫽ 12
(dollars per book)
Number of books bought ⫽ n (books)
Algebraic
Model
40 ⫺ 12n
When you buy 1 book, you have 40 ⫺ 12(1) ⫽ $28 left.
When you buy 3 books, you have 40 ⫺ 12(3) ⫽ $4 left.
Example 5
Simplifying by Combining Like Terms
4(x ⫹ 2) ⫺ 2(x ⫹ 2)
⫽ 4x ⫹ 8 ⫺ 2x ⫺ 4
⫽ (4x ⫺ 2x) ⫹ (8 ⫺ 4)
⫽ 2x ⫹ 4
Distributive property
Group like terms.
Combine like terms.
Checkpoint Complete the following exercises.
3. You have a $10 phone card. Each minute on the phone
costs 12 cents. Write an expression that shows how
much money is left on the card after x minutes on the
phone. Evaluate the expression for x ⫽ 20 and x ⫽ 60.
Homework
10 ⫺ 0.12x; $7.60; $2.80
4. Simplify the expression ⫺9j ⫺ j ⫹ 7j2.
7j2 ⫺ 10j
6
Algebra 2 Notetaking Guide • Chapter 1