1­2 Algebraic Expressions
August 26, 2008
1­2 algebraic expressions
Objectives:
To evaluate algebraic expressions
To simplify algebraic expressions
Jun 25­6:00 PM
1
1­2 Algebraic Expressions
August 26, 2008
Check the skills you'll need
Use the order of operations to simplify each expression.
. .
..
.
_
2
4. 3 8 + 12 4
1. 8 3 ­ 2 4
..
..
_
2. 8 ­ 4 + 6 3
_
2
5. 27 + 18 9 ­ 3 + 1
.. . ..
..
_
_
3. 24 12 4 3
_
3
6. (40 + 24) 8 ­ (2 + 1 )
* for help turn to page 873
Jun 25­6:03 PM
2
1­2 Algebraic Expressions
August 26, 2008
Vocabulary
variable
algebraic expression (variable expression) evaluate term
coefficient
Jun 25­6:03 PM
3
1­2 Algebraic Expressions
August 26, 2008
Evaluating an algebraic expression
Evaluate 3x ­ 2y + xy for x = 2 and y = ­ 1
3x ­ 2y + xy
Substitute 2 in for x and ­1 in for y
3(2) ­ 2(­1) + (2)(­1)
6 ­ (­2) + (­2)
Multiply first
6 + 2 + (­2)
To subtract, add the opposite
8 + (­2)
Add from left to right
6
Add
Jun 25­6:03 PM
4
1­2 Algebraic Expressions
August 26, 2008
Properties for Simplifying Algebraic Expressions
Let a, b, and c represent real numbers
Definition of Subtraction
a ­ b = a + (­b)
Definition of Division
_a
1_
_
a b = = a , b = 0
b
b
Distributive Property for Subtraction
a(b ­ c) = ab ­ ac
..
.
Multiplication by ­1
.
.
­1 a = ­1
Opposite of a Sum
­(a + b) = ­a + (­b)
Opposite of a Difference
­(a ­ b) = b ­ a
Opposite of a Product
­(ab) = ­a b = a (­b)
Opposite of an Opposite
­(­a) = a
Multiplication by 0
0 a = 0
.
.
Jun 25­6:03 PM
5
1­2 Algebraic Expressions
August 26, 2008
Simplifying Algebraic Expressions
Simplify by combining like terms
­2(a + b) + 5a ­ 3b
­2a ­ 2b + 5a ­ 3b
Distributive property
­2a + 5a ­ 2b ­ 3b
Commutative property of addition
­2a + 5a ­ (2b + 3b)
Opposite of a sum
(­2 + 5)a ­ (2 + 3)b
Distributive property
3a ­ 5b
Addition
Jun 25­6:03 PM
6
1­2 Algebraic Expressions
August 26, 2008
Finding Perimeter
Find the perimeter of each figure. Simplify the answer.
4x ­ 2y
y
y
2x + y
2x
4x ­ y
Jun 25­6:03 PM
7
1­2 Algebraic Expressions
August 26, 2008
homework
page: 15 ­ 17
#'s: 4 ­ 84, multipls of 4
Jun 25­6:03 PM
8