INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

Professor Fraser

Multiplying Monomials

Slide Duration:

Section 1: Basic Concepts
Variables and Expressions

24m 5s

Intro
0:00
Definitions
0:20
Variable
0:27
Algebraic Expression
2:21
Arithmetic Operations
2:27
Lecture Example 1
7:16
Lecture Example 2
8:27
-1
-2
Order of Operations

22m 16s

Intro
0:00
Why We Need It
0:15
Example: Order of Operations
1:25
Procedure To Evaluate
3:22
Lecture Example 1
6:45
Lecture Example 2
10:55
-1
-2
The Distributive Property

16m 27s

Intro
0:00
The Distributive Property
0:20
Extension to Several Numbers
2:05
Lecture Example 1
2:50
Lecture Example 2
5:15
-1
-2
The Real Number System

22m 35s

Intro
0:00
The Real Number System
0:21
Natural Numbers
0:22
Whole Numbers
0:37
Integers
1:06
Rational Numbers
1:35
Example: Decimals
2:07
The Real Number System, Cont.
5:00
Square Roots
5:10
Principle Square Root
6:04
Irrational Numbers
6:35
The Real Number System, Cont.
9:11
Picture Representation
9:25
Lecture Example 1
11:54
Lecture Example 2
14:10
-1
-2
Functions and Graphs

27m 49s

Intro
0:00
Functions
0:30
Definition
0:30
Example: Square Roots
1:18
Example: Gas Prices
3:20
Graphs
4:03
Definition
4:03
Example: Square Roots
4:48
Domain and Range
9:30
Definition
9:30
Example: Square Roots
10:01
Lecture Example 1
11:22
Lecture Example 2
13:58
-1
-2
Section 2: Solving Linear Equations
From Sentences to Equations

22m 13s

Intro
0:00
Strategy
1:40
Using Variables
1:55
Translating Phrases
2:18
Equality
3:00
Lecture Example 1
3:52
Lecture Example 2
8:36
-1
-2

14m 39s

Intro
0:00
Techniques
0:22
0:28
Example
0:47
Subtracting the Same Number
1:50
Example
1:54
Strategy
2:36
Isolate the Variable
2:46
Lecture Example 1
3:48
Lecture Example 2
5:41
-1
-2
Multiplication and Division Techniques

19m 19s

Intro
0:00
Techniques
0:16
Multiplied by the Same Number
0:18
Example
0:26
Divided by the Same Number
1:23
Non-zero Exception
1:28
Dividing by Zero
2:17
Example
3:01
Strategy
3:51
Isolate the Variable
3:55
Lecture Example 1
4:55
Lecture Example 2
6:40
-1
-2
Techniques for Multi-Step Equations

19m 13s

Intro
0:00
What are Multi-step Equations?
0:08
Strategy
0:30
Opposite Operations
0:50
Last Operation
1:18
Lecture Example 1
1:54
Lecture Example 2
4:16
-1
-2
When the Variable is on Both Sides of the Equation

24m 16s

Intro
0:00
Solving More Complicated Equations
0:17
Distributive Property and Grouping Symbols
0:36
Combining
0:51
Moving Variables to One Side
1:06
Posibble Outcomes
1:50
Exactly One Solution
2:02
No Solution
2:35
Example
2:51
Identities-True for All Real Numbers
4:26
Example
4:45
Lecture Example 1
6:17
Lecture Example 2
9:39
-1
-2
Ratios and Proportions

22m 39s

Intro
0:00
Definitions
0:16
Ratio
0:21
Proportion
0:56
Example
1:13
Cross Products
3:00
Example: Original Proportion
3:12
Example 2
5:24
Rates
6:55
Example: Gas
7:22
Example 2: Apples
7:43
Example 3: Speed
8:16
8:46
Lecture Example 1
9:17
Lecture Example 2
11:53
-1
-2
Applications of Percents

20m 38s

Intro
0:00
Definitions
0:22
Percent of Change
0:23
Percent of Increase
0:42
Percent of Decrease
0:55
Examples of Percent of Change
1:14
Sales Tax
1:21
Discount
1:57
Lecture Example 1
2:51
Lecture Example 2
4:46
-1
-2
More Than One Variable

22m 34s

Intro
0:00
More Than One Variable
0:21
Strategy
1:02
Typical Application
1:33
Example: Circumference
1:48
Example: Perimeter
2:21
Lecture Example 1
2:53
Lecture Example 2
5:43
-1
-2
Section 3: Functions
Relations

24m 39s

Intro
0:00
Definition
0:17
List, Table, Graph
0:42
Example: List
0:56
Example: Table
2:00
Example: Graph
2:47
Domain and Range
4:10
Inverse of a Relation
5:01
Example
5:21
Lecture Example 1
7:26
Lecture Example 2
10:39
-1
-2
Functions

19m 3s

Intro
0:00
Definition
0:21
Function
0:24
Example: Relation
0:50
Vertical Line Test
1:48
Example: Pass
2:02
Example 2: Fail
3:32
Example 3: Fail
4:18
Function Notation
5:33
Proper Notation
5:43
Example
6:29
Domain and Range
7:32
Lecture Example 1
8:06
Lecture Example 2
9:39
-1
-2
Linear Functions

20m 3s

Intro
0:00
Definition
0:12
Linear Equation
0:15
Example: A and B not zero
0:27
Example: B is zero
0:58
Example: A is zero
1:13
Graph and Intercepts
1:43
Straight Line
1:52
x-intercepts, y-intercepts
2:19
Example: Intercepts
2:27
Graphing Linear Equations
4:19
Example
4:40
Linear Functions
7:23
Example
8:00
Lecture Example 1
10:11
Lecture Example 2
12:42
-1
-2
Section 4: Linear Functions and their Graphs
Slope and Rate of Change

23m 58s

Intro
0:00
Rate of Change
0:27
Independent Variable
0:37
Dependent Variable
0:51
Slope
2:02
Example
2:19
Steepness of the Line
4:56
Possible Slopes
5:58
Positive
6:13
Negative
6:34
Zero
6:50
Undefined
7:11
Lecture Example 1
8:03
Lecture Example 2
10:34
-1
-2
Direct Variation

13m 18s

Intro
0:00
Definitions
0:13
Direct Variation
0:14
Constant of Variation
0:26
Graph
1:02
Example: Positive and Negative k
1:18
Applications
1:49
Lecture Example 1
2:16
Lecture Example 2
4:39
-1
-2
Slope Intercept Form of an Equation

17m 11s

Intro
0:00
Slope Intercept Form
0:16
Example
0:37
Lecture Example 1
2:24
Lecture Example 2
5:43
-1
-2
Point Slope Form of an Equation

10m 32s

Intro
0:00
Point Slope Form
0:11
Example
0:50
Lecture Example 1
2:03
Lecture Example 2
3:03
-1
-2
Parallel and Perpendicular Lines

18m 15s

Intro
0:00
Parallel Lines
0:12
Example: Non-vertical Lines
0:32
Perpendicular lines
1:57
Example: Slope Product is -1
2:15
Negative Reciprocal
3:08
Lecture Example 1
3:58
Lecture Example 2
7:12
-1
-2
Section 5: Systems of Equations
Graphing Systems of Equations

20m 1s

Intro
0:00
System of Equations
0:09
Definition
0:15
Solution
0:59
Solving by Graphing
1:27
Example
2:33
Number of Solutions
3:37
Independent
3:58
Dependent
4:03
Inconsistent
4:08
Example: 1 Solution
4:15
Example: No Solution
4:34
Example: Infinite Solution
4:51
Lecture Example 1
5:39
Lecture Example 2
8:51
-1
-2
Solving by Substitution

24m 12s

Intro
0:00
Substitution
0:17
Example
0:51
Number of Solutions
1:43
Infinite Solutions
2:14
No Solutions
2:50
Lecture Example 1
3:40
Lecture Example 2
6:56
-1
-2

12m 18s

Intro
0:00
Fundamental Principle
0:18
0:50
Lecture Example 1
1:23
Lecture Example 2
4:03
-1
-2
Solving by Multiplication

19m 11s

Intro
0:00
Fundamental Principle
0:24
Multiplication
0:28
Lecture Example 1
1:40
Lecture Example 2
6:36
-1
-2
Applications: Systems of Equations

18m 24s

Intro
0:00
Solving Systems of Equations
0:08
Graphing
0:32
0:50
Subtraction
1:04
Multiplication
1:13
Substitution
1:30
Lecture Example 1
3:20
Lecture Example 2
4:27
-1
-2
Section 6: Inequalities

10m 8s

Intro
0:00
Fundamental Principle
0:11
Solutions of Inequalities
0:55
Inequality
1:02
Set Builder Notation
1:13
Example
1:15
Graph on a Number Line
2:13
Lecture Example 1
3:29
Lecture Example 2
5:14
-1
-2
Inequalities: Multiplication and Division Techniques

10m 59s

Intro
0:00
Fundamental Principle
0:11
Example: Positive Number
0:51
Fundamental Principle
1:35
Example: Negative Number
1:50
Lecture Example 1
4:05
Lecture Example 2
5:12
-1
-2
Techniques for Multi-Step Inequalities

16m 21s

Intro
0:00
Similarity to Multi-step Equations
0:15
Inequalities Containing Grouping Symbols
1:03
Special Cases
1:26
Solution: All Real Numbers
1:40
Solution: Empty Set
2:16
Lecture Example 1
2:54
Lecture Example 2
4:37
-1
-2
Compound Inequalities

23m

Intro
0:00
Inequalities Combined by 'And'
0:12
Three Ways to Write Solution Set
1:41
Set Notation
2:01
Inequalities
2:12
Graph
2:29
Examples
2:31
Inequalities Combined by 'Or'
4:45
Example
5:59
Lecture Example 1
7:40
Lecture Example 2
10:55
-1
-2
Equations with Absolute Values

23m 13s

Intro
0:00
Absolute Value
0:15
Example: Distance
1:00
Absolute Value Function
2:34
Example
3:05
Lecture Example 1
4:57
Lecture Example 2
8:28
-1
-2
Inequalities with Absolute Values

17m 34s

Intro
0:00
Inequalities of the Form |x|< n
0:22
Inequalities of the Form |x|> n
3:30
Lecture Example 1
5:33
Lecture Example 2
8:50
-1
-2
Graphing Inequalities with Two Variables

30m 50s

Intro
0:00
Graph
0:22
Half-Plane
0:28
Boundary
1:37
Technique for Graphing
3:14
Example
4:01
Dashed Line
5:13
Solid Line
6:30
Technique for Graphing, cont.
8:58
Example
9:09
Lecture Example 1
12:19
Lecture Example 2
15:48
-1
-2
Graphing Systems of Inequalities

27m 38s

Intro
0:00
System of Inequalities
0:26
Example
0:43
Solving a System of Inequalities
1:17
Example
1:41
Lecture Example 1
2:58
Lecture Example 2
7:22
-1
-2
Section 7: Polynomials
Multiplying Monomials

19m 55s

Intro
0:00
What is a Monomial?
0:43
Constant
1:11
Power
1:48
Exponent and Base
2:39
Properties of Exponents
3:02
Simplified Form
5:52
Each Base Appears Exactly Once
6:02
No Powers of Powers
6:18
All Fractions Simplified
6:33
Lecture Example 1
6:43
Lecture Example 2
8:12
-1
-2
Dividing Monomials

23m 9s

Intro
0:00
Properties of Exponents
0:26
Example
1:07
Properties of Exponents, cont
2:18
Example
3:18
Properties of Exponents, cont
4:55
Example
5:32
Properties of Exponents, cont
8:49
Lecture Example 1
11:43
Lecture Example 2
13:13
-1
-2
Polynomials

16m 35s

Intro
0:00
What is a Polynomial
0:45
Monomial
0:47
Example: Trinomial
1:46
Trinomial
2:10
Example: Binomial
2:21
Binomial
2:30
Degree of a Polynomial
4:28
Example
4:40
Ordering Polynomials
6:45
Example
7:27
Lecture Example 1
9:27
Lecture Example 2
10:31
-1
-2

22m

Intro
0:00
0:36
Like Polynomials
0:48
Example
1:04
Subtracting Polynomials
3:55
Example
4:01
Lecture Example 1
5:30
Lecture Example 2
8:04
-1
-2
Multiplying Polynomials by Monomials

24m 8s

Intro
0:00
Distributive Property
0:22
Basic Principle
0:42
Example
1:04
Solving Equations
3:25
Lecture Example 1
4:26
Lecture Example 2
7:51
-1
-2
Multiplying Polynomials

26m 37s

Intro
0:00
Distributive Property
0:23
Example
0:34
Example
1:55
Foil Method
5:17
Lecture Example 1
7:44
Lecture Example 2
10:15
-1
-2
Special Products

19m 40s

Intro
0:00
Square of a Sum
0:12
Perfect Square Trinomial
1:43
Example
2:13
FOIL Technique
3:09
Square of a Difference
3:38
Example
5:27
Difference of Two Squares
6:12
Example
7:43
Lecture Example 1
8:51
Lecture Example 2
11:06
-1
-2
Section 8: Factoring
Factoring Monomials

27m 25s

Intro
0:00
Prime and Composite Numbers
1:01
Prime Number
1:23
Composite Number
3:03
Factored Forms
4:07
Prime Factored Form
4:19
Factored Form
5:40
Greatest Common Factor (GCF)
7:41
Example
8:00
GCF of Monomials
10:07
Example
10:18
Lecture Example 1
12:52
Lecture Example 2
17:08
-1
-2
Factoring Using Greatest Common Factor (GCF)

26m 3s

Intro
0:00
Distributive Property
0:19
Factor Out an Expression
1:21
Example
2:52
Factoring by Grouping
4:40
Example
6:00
Zero Product Property
8:24
Example
9:03
Lecture Example 1
11:19
Lecture Example 2
14:19
-1
-2
Factoring Trinomials with Leading Coefficient 1

27m 37s

Intro
0:00
Factoring Trinomials
0:23
Example
2:06
Rules for Signs
6:27
Both Positive
6:41
Both Negative
7:00
Opposite Signs
7:33
Solving Equations
8:26
Example
8:59
Lecture Example 1
11:14
Lecture Example 2
14:01
-1
-2
Factoring General Trinomials

34m 11s

Intro
0:00
Factoring Trinomials
0:40
Example: List
1:38
Grouping
5:46
Example
5:55
Rules for Signs
9:04
Example
9:22
Greatest Common Factor (GCF)
10:29
Prime Polynomials
11:03
Example
11:32
Solving Equations
12:32
Lecture Example 1
13:11
Lecture Example 2
18:37
-1
-2
Factoring the Difference of Two Squares

20m 22s

Intro
0:00
Difference of Two Squares
0:40
Example
1:56
Factoring Using Several Techniques
3:33
Solving Equations
4:11
Lecture Example 1
4:55
Lecture Example 2
6:05
-1
-2
Factoring Perfect Squares

18m 7s

Intro
0:00
Perfect Squares
0:10
Perfect Square Trinomials
1:17
Solving Equations
2:53
Square Root Property
2:58
Example
3:06
Lecture Example 1
4:23
Lecture Example 2
6:56
-1
-2

28m 5s

Intro
0:00
Parabolas
0:09
Parabolas That Open Upward
3:58
Minimum
4:26
Parabolas That Open Downward
4:54
Maximum
5:09
Vertex
7:28
Example
8:01
Axis of Symmetry
11:03
Lecture Example 1
13:27
Lecture Example 2
17:17
-1
-2
Solving Equations by Graphing

28m 18s

Intro
0:00
0:22
Example
0:50
Two Distinct Solutions/Roots
5:08
One Double Root
5:58
No Real Roots
7:14
Estimating Solutions
8:00
Example
8:16
Example
8:31
Lecture Example 1
9:43
Lecture Example 2
14:10
-1
-2
Solving Equations by Completing the Square

25m 7s

Intro
0:00
Perfect Square Trinomials
0:22
Example
1:12
Completing the Square
3:17
Example
3:25
Solving Equations
6:12
Example
6:27
8:25
Lecture Example 1
10:23
Lecture Example 2
14:17
-1
-2
Solving Equations Using the Quadratic Formula

24m 15s

Intro
0:00
1:26
Example
2:23
Discriminant
4:28
Two Distinct Real Roots
5:07
One Double Real Root
5:23
No Real Root
5:42
Why Does It Work?
6:05
Lecture Example 1
7:53
Lecture Example 2
11:50
-1
-2
Section 10: Radical Expressions and Equations

32m 40s

Intro
0:00
0:14
0:28
Example
0:32
Simplest Form
1:07
Example
1:35
Product Property
2:34
Verifications
2:47
Square Roots of Variables with Even Powers
4:27
Quotient Rule
6:45
Example
6:55
Rationalizing Denominators
7:32
Example
7:41
Conjugates
10:44
Examples
10:59
14:44
Example
15:39
Lecture Example 1
17:34
Lecture Example 2
19:38
-1
-2

19m 59s

Intro
0:00
0:12
Example
0:19
1:53
Example
2:07
Lecture Example 1
5:29
Lecture Example 2
6:36
-1
-2

26m 50s

Intro
0:00
0:22
Example
0:33
2:04
Example
2:16
Extraneous Solutions
3:14
Example
4:31
Lecture Example 1
7:33
Lecture Example 2
9:45
-1
-2
Pythagorean Theorem

19m 8s

Intro
0:00
Right Triangles
0:51
Right Angle
1:03
Vertex
1:11
Symbol
1:16
Hypotenuse and Legs
1:42
Pythagorean Theorem
2:27
Example
2:47
Example
3:12
Pythagorean Triples
4:03
Converse of the Pythagorean Theorem
6:39
Example
7:41
Lecture Example 1
8:57
Lecture Example 2
10:05
-1
-2
Distance Formula

18m 27s

Intro
0:00
Distance Formula
0:17
Missing Coordinates
1:46
Example
1:55
Lecture Example 1
4:10
Lecture Example 2
5:57
-1
-2
Section 11: Rational Expressions and Equations
Inverse Variation

14m 43s

Intro
0:00
Inverse Variation
0:23
Constant of Variation
0:37
Graphing Inverse Variation
1:08
Example: Hyperbola
1:15
Product Rule
3:54
Lecture Example 1
5:31
Lecture Example 2
7:43
-1
-2
Rational Expressions

32m 43s

Intro
0:00
Rational Expression
0:55
Example
1:03
Excluded Values
1:29
Examples
1:40
Simplifying Rational Expressions
5:36
Greatest Common Factor (GCF)
5:46
Example
5:55
Example
7:42
Simplifying and Excluded Values
9:34
Lecture Example 1
9:50
Lecture Example 2
13:55
-1
-2
Multiplying Rational Expressions

27m 22s

Intro
0:00
Procedure
0:16
Example
0:33
Cancel Before Multiplication
3:44
Example
3:55
Rational Expressions Containing Polynomials
6:19
Example
6:26
Lecture Example 1
11:09
Lecture Example 2
15:39
-1
-2
Dividing Rational Expressions

28m 30s

Intro
0:00
Procedure
0:21
Example
0:59
Cancel Before Multiplication
4:31
Example
4:39
Rational Expressions Containing Polynomials
8:01
Example
8:08
Lecture Example 1
10:43
Lecture Example 2
13:46
-1
-2
Dividing Polynomials

29m 44s

Intro
0:00
Dividing a Polynomial by a Monomial
1:07
Example
1:14
Dividing a Polynomial by a Binomial
3:30
Example
3:51
Long Division
5:20
Example
6:25
Missing Terms
11:11
Example
12:25
Lecture Example 1
14:54
Lecture Example 2
16:35
-1
-2
Adding and Subtracting Rational Expressions with Like Denominators

16m 50s

Intro
0:00
0:14
Example
0:41
Subtraction with Like Denominators
2:23
Example
2:30
2:55
Example
3:03
Lecture Example 1
6:41
Lecture Example 2
7:09
-1
-2
Adding and Subtracting Rational Expressions with Unlike Denominators

36m

Intro
0:00
Least Common Multiple (LCM) of Polynomials
0:34
Example
0:45
Example
1:55
4:08
Example
4:45
Lecture Example 1
8:13
Lecture Example 2
10:22
-1
-2
Complex Fractions

18m 43s

Intro
0:00
Mixed Expression
0:08
Example
0:30
Complex Fraction
2:45
Example
2:57
Example
3:11
Example
3:22
Simplifying Complex Fractions
3:58
Why Does It Work?
4:22
Lecture Example 1
4:48
Lecture Example 2
8:44
-1
-2
Rational Equations

39m 10s

Intro
0:00
Definition
0:08
Examples
0:17
Solving Rational Expressions
3:02
Example
3:09
Work Problems
6:31
Example
6:48
Extraneous Solutions
13:12
Example
14:13
Lecture Example 1
17:21
Lecture Example 2
19:59
-1
-2
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• ## Related Books

### Multiplying Monomials

• A monomial is a product of a number and zero or more variables. If there are no variables, the monomial is called a constant.

• A power is an expression of the form xn, where n is a positive integer. The variable x is called the base and the number n is called the exponent.

• Recall from earlier work the laws of exponents: an· am = am+n, (am)n = amn, and

• (ab)m = ambm.

• An expression is considered to be in simplified form if each base is used exactly once, there are no powers of powers, and all fractions are in simplified form.

• You will often be asked to convert a given expression into simplified form.

### Multiplying Monomials

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What is a Monomial? 0:43
• Constant
• Power
• Exponent and Base
• Properties of Exponents 3:02
• Simplified Form 5:52
• Each Base Appears Exactly Once
• No Powers of Powers
• All Fractions Simplified
• Lecture Example 1 6:43
• Lecture Example 2 8:12

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