Download Identify like terms

3-2 Simplifying Algebraic Expressions
Preview
Evaluating Algebraic Expressions
Warm Up
California Standards
Lesson Presentation
3-2 Simplifying Algebraic Expressions
Evaluating Algebraic Expressions
Warm Up
Simplify.
1.
2.
3.
4.
9 + 13  5 + 3 20
16  8 + 4  1 11
6 + 9  10 + 3 8
17 + 8  20  2 3
3-2 Simplifying Algebraic Expressions
Evaluating Algebraic Expressions
California
Standards
AF1.3 Simplify numerical expressions
by applying properties of rational numbers (e.g.
identity, inverse, distributive, associative,
commutative) and justify the process used.
3-2 Simplifying Algebraic Expressions
Evaluating
Algebraic Expressions
Vocabulary
term
like term
coefficient
constant
equivalent expression
3-2 Simplifying Algebraic Expressions
In the expression below, 7x, 5, 3y, and 2x are
Evaluating
Expressions
terms.
A term canAlgebraic
be a number, a
variable, or
a product of numbers and variables. Terms in
an expression are separated by plus or minus
signs.
Constant
Coefficients
3-2 Simplifying Algebraic Expressions
Name
Definition
Example
term
A term can be a number, a
variable, or a product of numbers
and variables
7x, 5, 3y, and
2x
Like Term
Like Terms have the same
variable raised to the same
power
Ex 1: 3a, 5a
Ex 2: 9x, 5x
constant
A constant is a number that does
not change
4, 0.75, and 11
coefficient
A coefficient is a number that is
multiplied by a variable in an
algebraic expression
7 in (7x), 5 in 5a
Equivalent expressions
Equivalent expressions - have
the same value for all values of
the variables
Ex 1) 3x + 3,
3 ( x +1)
Evaluating Algebraic Expressions
3-2 Simplifying Algebraic Expressions
Additional Example 1: Combining Like Terms in
One-Variable Expressions
Evaluating Algebraic Expressions
Combine like terms.
A. 14a – 5a
9a
Identify like terms.
B. 7y + 8 – 3y – 1 + y
Identify like terms; the
coefficient of y is 1, because
1y = y.
5y + 7
Combine coefficients: 14 – 5 = 9
Combine coefficients: 7 – 3 + 1 = 5
and 8 – 1 = 7
3-2 Simplifying Algebraic Expressions
Evaluating Algebraic Expressions
Helpful Hint
When you rearrange terms, move the
operation in front of each term with that
term.
3-2 Simplifying Algebraic Expressions
Additional Example 2A: Combining Like Terms in
Two-Variables Expressions
Evaluating Algebraic Expressions
Combine like terms.
9x + 3y – 2x + 5
9x + 3y – 2x + 5
Identify like terms.
7x + 3y + 5
Combine coefficients: 9 – 2 = 7
3-2 Simplifying Algebraic Expressions
Additional Example 2B: Combining Like Terms in
Two-Variable Expressions
Evaluating Algebraic Expressions
Combine like terms.
4m + 9n – 2
4m + 9n – 2
No like terms.
3-2 Simplifying Algebraic Expressions
Evaluating Algebraic Expressions
To simplify an expression, perform all
possible operations, including
combining like terms. You may need to
use the Associative, Commutative, or
Distributive Properties.
3-2 Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive
Property to Simplify
Evaluating Algebraic Expressions
Simplify 6(5 + n) – 2n.
6(5 + n) – 2n
6(5) + 6(n) – 2n
Distributive Property
30 + 6n – 2n
Multiply.
30 + 6n – 2n
Identify like terms.
30 + 4n
Combine coefficients: 6 – 2 = 4.
3-2 Simplifying Algebraic Expressions
Check It Out! Examples
Combine like terms.
Evaluating Algebraic Expressions
A. 2x + 5x – 4y + 3
2x + 5x – 4y + 3
Identify like terms.
7x – 4y + 3
Combine coefficients: 2 + 5 = 7
B. 9d + 7c – 4d – 2c
9d + 7c – 4d – 2c
Identify like terms.
5d + 5c
Combine coefficients: 9 – 4 = 5
and 7 – 2 = 5
C. 8g + c – 6
8g + c – 6
No like terms.
3-2 Simplifying Algebraic Expressions
Evaluating Algebraic Expressions
Open Workbook
Review for Mastery
Page 19
Start working.