MATH 1111 College Algebra

1
MATH 1111 College Algebra

• Review of Basic Concepts

2
Sets of Numbers

• Natural Numbers
• Integers
• Rational Numbers
• Irrational Numbers
• Real Numbers

3
Properties of Addition

• Commutative
• Associative
• Identity
• Inverse

4
Properties of Multiplication

• Commutative
• Associative
• Identity
• Inverse

5
The Distributive Property
6
A Word about Exponents

• aman amn
• am/an am-n
• a0 1, if a ? 0
• a-n 1/an, if a ? 0
• (am)n amn
• (a/b)n an/bn if b ? 0

7
The nth root of a number

• If bn a, n a positive integer, b is called an
  nth root of a.
• The principal nth root of a has the same sign as
  a and is denoted by ?

8
Some Special Products

• First, outer, inner, last
• (ab)(ab) a2b2
• (a?b)2 a2?2abb2
• (a b)(a2abb2) a3b3
• (a-b)(a2abb2) a3-b3
• (a?b)3 a3 ?3a2b3ab2 ?b3