Download Evaluate and Simplify Algebraic Expressions

1.2
Evaluate and Simplify
Algebraic Expressions
Goal
Your Notes
p Evaluate and simplify expressions involving real
numbers.
VOCABULARY
Power
Variable
Term
Coefficient
Identity
ORDER OF OPERATIONS
1 1 72 p (5 2 3)
Step 1 First, do operations
that occur within
.
.
Step 2 Next, evaluate
5 1 1 72 p 2
Step 3 Then, do multiplications
and divisions from
.
5 1 1 49 p 2
Step 4 Finally, do additions
and subtractions from
.
5 1 1 98
5 99
4
Lesson 1.2 • Algebra 2 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
1.2
Evaluate and Simplify
Algebraic Expressions
Goal
Your Notes
p Evaluate and simplify expressions involving real
numbers.
VOCABULARY
Power An expression formed by repeated
multiplication of the same factor
Variable A letter that is used to represent one or
more numbers
Term In an expression that can be written as a
sum, the parts added together are called terms.
Coefficient When a term is a product of a number
and a power of a variable, the number is called the
coefficient of the power.
Identity A statement that equates two equivalent
expressions
ORDER OF OPERATIONS
Step 1 First, do operations
that occur within
grouping symbols .
1 1 72 p (5 2 3)
Step 2 Next, evaluate powers .
5 1 1 72 p 2
Step 3 Then, do multiplications
and divisions from
left to right .
5 1 1 49 p 2
Step 4 Finally, do additions
and subtractions from
left to right .
5 1 1 98
5 99
4
Lesson 1.2 • Algebra 2 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Your Notes
Example 1
Evaluate an algebraic expression
Evaluate 26y 2 2 11y 1 34 when y 5 25.
Solution
26y 2 2 11y 1 34
5 26(
)2 2 11(
5 26(
) 2 11(
5
1
) 1 34
) 1 34
1 34
Substitute 25 for y.
Evaluate the power.
Multiply.
5
Add.
Checkpoint Evaluate the expression.
1. 3a 2 16 when a 5 7
2. 2y 2(y 2 10) when y 5 3
TERMS AND COEFFICIENTS
In an expression that can be written as a sum, the
parts added together are called
.
A term that has a variable part is a
A term that has no variable part is a
.
.
When a term is a product of a number and a power
of a variable, the number is called the
of the power.
Copyright © Holt McDougal. All rights reserved.
Lesson 1.2 • Algebra 2 Notetaking Guide
5
Your Notes
Example 1
Evaluate an algebraic expression
Evaluate 26y 2 2 11y 1 34 when y 5 25.
Solution
26y 2 2 11y 1 34
5 26( 25 )2 2 11( 25 ) 1 34
Substitute 25 for y.
5 26( 25 ) 2 11( 25 ) 1 34
Evaluate the power.
5 2150 1 55 1 34
Multiply.
5 261
Add.
Checkpoint Evaluate the expression.
1. 3a 2 16 when a 5 7
5
2. 2y 2(y 2 10) when y 5 3
2126
TERMS AND COEFFICIENTS
In an expression that can be written as a sum, the
parts added together are called terms .
A term that has a variable part is a variable term .
A term that has no variable part is a constant term .
When a term is a product of a number and a power
of a variable, the number is called the coefficient
of the power.
Copyright © Holt McDougal. All rights reserved.
Lesson 1.2 • Algebra 2 Notetaking Guide
5
Your Notes
Example 2
Simplify by combining like terms
a. 11x 2 5x
b. 2(y 1 5) 2 3( y 2 9)
c. 14x 2 6y 1 5x 1 13y
Solution
a. 11x 2 5x 5 (
)x
Distributive
property
5
Add coefficients.
b. 2(y 1 5) 2 3( y 2 9)
5 2y 1 10 2 3y 1 27
5(
5
)1(
Distributive
property
)
Group like
terms.
1
Combine like
terms.
c. 14x 2 6y 1 5x 1 13y
)1(
5(
5
)
1
Group like
terms.
Combine like
terms.
Checkpoint Simplify the expression.
Homework
6
3. 11n 2 6 1 14 2 2n
4. 2a3 2 6a2 1 5a3
5. 6(x 2 4) 2 3(x 1 11)
6. 215y 1 12x 1 2y 2 7x
Lesson 1.2 • Algebra 2 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Your Notes
Example 2
Simplify by combining like terms
a. 11x 2 5x
b. 2(y 1 5) 2 3( y 2 9)
c. 14x 2 6y 1 5x 1 13y
Solution
a. 11x 2 5x 5 ( 11 2 5 )x
Distributive
property
5 6x
Add coefficients.
b. 2(y 1 5) 2 3( y 2 9)
5 2y 1 10 2 3y 1 27
Distributive
property
5 ( 2y 2 3y ) 1 ( 10 1 27 )
Group like
terms.
5 2y 1 37
Combine like
terms.
c. 14x 2 6y 1 5x 1 13y
5 ( 14x 1 5x ) 1 ( 26y 1 13y )
Group like
terms.
5 19x 1 7y
Combine like
terms.
Checkpoint Simplify the expression.
3. 11n 2 6 1 14 2 2n
9n 1 8
Homework
5. 6(x 2 4) 2 3(x 1 11)
3x 2 57
6
Lesson 1.2 • Algebra 2 Notetaking Guide
4. 2a3 2 6a2 1 5a3
7a3 2 6a2
6. 215y 1 12x 1 2y 2 7x
213y 1 5x
Copyright © Holt McDougal. All rights reserved.