Math 0950

1
Math 0950

• McKeague PreAlg 4th Ed
• Chapter 2.6
• Simplifying Algebraic Expressions

2
Introduction

• In this section we want to combine some of the
  work we have done in this chapter and in Chapter
  1 to simplify expressions containing variables
  (algebraic expressions)

3
Associative Property

• Simplify
• 4(5x)
• 7(3a)
• -2(5x)
• 3(-4y)

4
Associative Property

• Simplify
• 3 (8 x)
• (2x 5) 10

5
Distributive Property

• The distributive property can be demonstrated by
  using the following symbols
• a ( b c )
• Since subtraction is defined as addition of the
  opposite, we can then use those rules with
  problems involving subtraction
• a ( b c )

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Examples

• 4 ( x 5 )
• 2 ( a 3 )
• 4 ( 5x 3)
• 7 ( 3a 6 )

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Examples

• 5 ( 2x 3y )
• 6 ( 4x 5 )
• 3 ( 8a 4 )
• 8 ( 3x 4y )

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Distributive Property (in reverse)

• Because multiplication is a commutative
  operation, we can re-write the distributive
  property like this
• b a c a
• We can now use this definition to simplify
  equations like the one below
• 4x 3x

9
Similar Terms

• Expressions like 4x and 3x are called similar
  terms because the variable parts are the same.
  Other examples include 5y and -6y and the terms
  ½a, 7a, and -13a. We can combine similar terms
  by using the distributive property

10
Example
11
Exponents and Variables

• Now lets work on simplifying expressions like
  2x(3x). Since this only involves multiplication,
  we can use the commutative property to change the
  order of the numbers and variables. We can also
  use the associative property to change the
  grouping of the numbers and variables. Together
  we can use these two methods to simplify the
  equation

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Exponents and Variables

• 2x(3x)
• Note that 6x2 means 6xx NOT 6x6x. The
  exponent (2 in this case) is only associated with
  the number to its left, unless parenthesis are
  used (i.e. (6x)2means 6x6x)

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Examples

• Expand and Simplify
• (5a)3
• (8xy)2
• (7x)2(8xy)2
• (2x)3(4x)2

14
Algebraic Expressions representing area and
perimeter

• Below are a square with sides of length s and a
  rectangle with length of l and width of w. The
  table that follows shows the algebraic
  expressions for each

15
Examples

• Find the area and parimeter of a square with a
  side 6 long.
• A soccer field is 100yds long and 75yds wide.
  Find the area and perimeter

16
Practice

• Problem set 2.6
• 1, 9, 13, 21, 29, 35, 37, 45, 49, 53, 55, 57,
  61, 65, 73, 77, 81, 85

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Assignment

• Problem Set 2.6
• 2-42 (every 4 2,6,10), 46 90 evens