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1.2 - Products. Commutative Properties. Addition:. Multiplication:. 1.2 - Products. Associative Properties. Addition:. Multiplication:. 1.2 - Products. Distributive Property of Multiplication. 1.2 - Products. Product Rule for Exponents.

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Presentation Transcript
slide2

1.2 - Products

Commutative Properties

Addition:

Multiplication:

slide3

1.2 - Products

Associative Properties

Addition:

Multiplication:

slide4

1.2 - Products

Distributive Property of Multiplication

slide5

1.2 - Products

Product Rule for Exponents

If m and n are positive integers and a is a real number, then

Examples:

slide6

1.2 - Products

Power Rule for Exponents

If m and n are positive integers and a is a real number, then

Examples:

slide7

1.2 - Products

Power of a Product Rule

If m, n, and r are positive integers and a and b are real numbers, then

Examples:

slide8

1.2 - Products

Multiplying Monomials by Monomials

Examples:

slide9

1.2 - Products

Multiplying Monomials by Polynomials

Examples:

slide10

1.2 - Products

Multiplying Two Binomials using FOIL

First terms

Outer terms

Inner terms

Last terms

slide11

1.2 - Products

Multiplying Two Binomials using FOIL

First terms

Outer terms

Inner terms

Last terms

slide12

1.2 - Products

Squaring Binomials

slide13

1.2 - Products

Multiplying Two Polynomials

Examples:

slide14

1.3 – Sums and Differences

Algebraic Expression - A combination of operations on variables and numbers.

Evaluate the following:

slide15

1.3 – Sums and Differences

Evaluate the following:

slide16

1.3 – Sums and Differences

Simplify each polynomial.

slide17

1.3 – Sums and Differences

Simplify each polynomial.

slide18

1.4 - Factorizations

A Number as a Product of Prime Numbers

Factor Trees

slide19

1.4 - Factorizations

A Number as a Product of Prime Numbers

Factor Trees

slide20

1.4 - Factorizations

A Number as a Product of Prime Numbers

factoring by grouping

1.4 - Factorizations

+

+

10x

+

2x

4x2

5

Factoring by Grouping

factoring by grouping1

1.4 - Factorizations

-

-

8x

+

3x

2x2

12

Factoring by Grouping

factoring by grouping2

1.4 - Factorizations

-

+

14x

-

10x

35x2

4

Factoring by Grouping

factoring trinomials

1.4 - Factorizations

Factors of 50 are:

1, 50

5,10

2, 25

Factoring Trinomials

factoring trinomials1

1.4 - Factorizations

3, 12

4, 9

6, 6

Factors of 36 are:

1, 36

2, 18

Factoring Trinomials

factoring trinomials2

1.4 - Factorizations

Factors of 9 are:

1, 9

3, 3

Factoring Trinomials

factoring trinomials3

1.4 - Factorizations

Product of 2 and 12:

24

Factors of 24 are:

2, 12

1, 24

3, 8

4, 6

Factoring Trinomials

Factors of 24 that combine to 11:

3, 8

-

-

8x

+

3x

2x2

12

factoring trinomials4

1.4 - Factorizations

Product of 12 and 3:

36

Factors of 36 are:

2, 18

4, 9

6, 6

1, 36

3, 12

Factoring Trinomials

Factors of 36 that combine to 16:

2, 18

+

-

18ab

3b2

12a2

2ab

-

slide29

1.4 - Factorizations

The Difference of Two Squares

Not the difference

slide30

1.4 - Factorizations

The Difference of Two Squares

slide31

1.4 - Factorizations

The Sum and Difference of Two Cubes

slide32

1.4 - Factorizations

The Sum and Difference of Two Cubes

1 5 quotients
1.5 – Quotients

What is the Rule?

Zero Exponent

slide34

1.5 – Quotients

Problem:

If a is a real number other than 0 and n is an integer, then

slide36

1.5 – Quotients

If a is a real number other than 0 and n is an integer, then

Examples:

1 5 quotients3
1.5 – Quotients

Practice Problems

1 5 quotients4
1.5 – Quotients

Practice Problems