Download 3-2 Simplify Expressions

3-2 Simplifying Algebraic Expressions
Warm Up
Evaluating Algebraic Expressions
Simplify.
1. 9 + 13 − 5 + 3
2. 16 − 8 + 4 − 1
3. 6 + 9 − 10 + 3
4. 17 + 8 − 20 − 2
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
terms.
A term can Algebraic
be a number, aExpressions
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
Like terms, such as 7x and 2x, can be grouped
together
because they
have the same
variable
Evaluating
Algebraic
Expressions
raised to the same power. Often, like terms have
different coefficients. A coefficient is a number
that is multiplied by a variable in an algebraic
expression. A constant is a number that does not
change. Constants, such as 4, 0.75, and 11, are
also like terms.
When you combine like terms, you change the
way an expression looks but not the value of the
expression. Equivalent expressions have the
same value for all values of the variables.
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
B. 7y + 8 – 3y – 1 + y
5y + 7
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
3-2 Simplifying Algebraic Expressions
Additional Example 2B: Combining Like Terms in
Two-Variable Expressions
Evaluating Algebraic Expressions
Combine like terms.
5t + 7p – 3p – 2t
5t + 7p – 3p – 2t
3-2 Simplifying Algebraic Expressions
Additional Example 2C: Combining Like Terms in
Two-Variable Expressions
Evaluating Algebraic Expressions
Combine like terms.
4m + 9n – 2
4m + 9n – 2
3-2 Simplifying Algebraic Expressions
Check It Out! Example 2
Combine like terms.
Evaluating Algebraic Expressions
A. 2x + 5x – 4y + 3
7x – 4y + 3
B. 9d + 7c – 4d – 2c
5d + 5c
C. 8g + c – 6
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.
3-2 Simplifying Algebraic Expressions
Check It Out! Example 3
Evaluating
Algebraic
Simplify
3(c + 7) –
c.
3(c + 7) – c
Expressions
3-2 Simplifying Algebraic Expressions
Lesson Quiz
Evaluating Algebraic Expressions
Combine like terms.
1. 3x + 4 + 2x
2. 13k + 6 − 8m + 9 + k
Simplify.
3. 4(3x + 6) − 7x
4. 6(x + 5) + 3x
Solve.
5. The accounting department ordered 15 boxes of
pens. The marketing department ordered 9 boxes of
pens. If the total cost of the combined order was
$72, what is the price of each box of pens?