Chapter 8.1.  Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems  Students will know how to apply.

Slides:

Advertisements

Similar presentations

Polynomials Chapter 8.4.

Advertisements

1 Topic Rules of Exponents. 2 Lesson California Standards: 2.0 Students understand and use such operations as taking the opposite, finding.

M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Chapter 8.6.

Properties of Exponents III Power to a Power Zero Power.

Multiplying Monomials and Raising Monomials to Powers

Chapter 8.5. C OMBINING L IKE T ERMS  Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems  Students.

1.Be able to divide polynomials 2.Be able to simplify expressions involving powers of monomials by applying the division properties of powers.

Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111.

Algebra I Chapter 10 Review

PRE-ALGEBRA. Lesson 4-7 Warm-Up PRE-ALGEBRA How do you multiply numbers with the same base? How do you multiply powers in algebraic expressions? Rule:

Lesson 8.4 Multiplication Properties of Exponents

Lesson 7-4 Warm-Up.

EXPONENTS. EXPONENTIAL NOTATION X IS THE BASE 2 IS THE EXPONENT OR POWER.

Lesson 1 MULTIPLYING MONOMIALS. What are we going to do…  Multiply monomials.  Simplify expressions involving powers of monomials.

5.2 Exponents Objectives The student will be able to: 1. Multiply monomials. 2. Simplify expressions with monomials. 3. Learn and apply the laws of exponents.

Do Now: Evaluate Multiplying Monomials Objectives SWBAT: 1) multiply monomials 2) Simplify expressions involving powers of monomials.

The Distributive Property allows you to multiply each number inside a set of parenthesis by a factor outside the parenthesis and find the sum or difference.

Powers of Products and Quotients (5-9). Powers of Products and Quotients (5-9)

1 ALGEBRA 1B UNIT 8 Multiplication Property of Exponents DAY 2.

Monomials Multiplying Monomials and Raising Monomials to Powers.

Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Math humor: Question: what has variables with whole-number exponents and a bunch.

BY: ANNA SMOAK Multiplying a Polynomial by a Monomial.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 4 Polynomials.

Exponent Rules and Multiplying Monomials Multiply monomials. 2.Multiply numbers in scientific notation. 3.Simplify a monomial raised to a power.

Multiplication of Exponents Notes

More Multiplication Properties of Exponents

Aim: How do we multiply a monomial by a monomial? Do Now: Multiply: 1. 3 · 3 · 3 2. x · x 3. 3x · 2x 4. x³ · x² 5. (4x 2 ) 2.

Collecting Like Terms Lesson 31. Terms Literal Coefficients – are variables (letters) that represent unknown numbers. Numerical coefficients – are numbers.

Problems of the Day Simplify each expression. 1. 9m 2 – 8m + 7m 2 2. (10r 2 + 4s 2 ) – (5r 2 + 6s 2 ) 3. (pq + 7p) + (6pq – 10p – 5pq) 4. (17d 2 – 4) –

8.3 – Multiplying Exponents

Warm Up What is each expression written as a single power?

ALGEBRA READINESS LESSON 10-2 Warm Up Lesson 10-2 Warm-Up.

Monomials Multiplying Monomials and Raising Monomials to Powers.

Distributive Property and combining like terms.. Use the Distributive Property to simplify each expression. 1. 8(m + 5) = (3x + 9) = –2(4.

A. – b. 8 – 19 c. – 15 – (– 15) d. – 10 + (– 46) Problems of the Day Simplify. e. f. g. h.

Warm Up: Simplify. Evaluating expressions 2/20/14 Objectives: – Understand and identify the terms associated with expressions – Determine the degree of.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 4 Polynomials.

Section 8.1.  Perfect Square: A number multiplied by itself , 9, 16, 25, 36, 47, 64, 81, 100, 121, 144…

12.01 Multiplying Monomials. A monomial is a number, a variable, or a product of both. Examples: 8, x, 5y, x 3, 4x 2, – 6xy 7 Exponential Notation amam.

D IVIDING M ONOMIALS Chapter 8.2. D IVIDING M ONOMIALS Lesson Objective: NCSCOS 1.01 Write equivalent forms of algebraic expressions to solve problems.

Chapter 7: Polynomials This chapter starts on page 320, with a list of key words and concepts.

EXPRESSIONS & EXPONENTS COORDINATE ALGEBRA. WHY DO WE USE VARIABLES AND WHAT IS THE SIGNIFICANCE OF USING THEM IN EXPRESSIONS AND EQUATIONS? We use variables.

LESSON 4-7 EXPONENTS & MULTIPLYING. When we multiply terms with exponents  ADD exponents of like variables.

7-1 Multiplying Monomials Part 4. x n x is the n is the Exponents.

Chapter 9.1. Factoring a number  Objective NCSCOS 1.01 – Write equivalent forms of algebraic expressions to solve problems  Students will know how to.

Monomials Lesson 5-1 Algebra 2. Vocabulary Monomials - a number, a variable, or a product of a number and one or more variables 4x, 20x 2 yw 3, -3, a.

In this lesson, we will multiply polynomials

The Distributive Property

Multiplying with exponents

Multiplication of Monomials

Chapter 9.1 Factoring a number.

7-4 More Multiplication Properties of Exponents

8.6 Multiplying a Polynomial by a Monomial

Combine Like Terms I can simplify expressions with several variables by combining like terms.

52 Exponent Base 52 · 53 = 55 If the numerical bases are the same, keep the base and add the exponents.

Multiplying Polynomials

Dividing Monomials.

Multiplying and Dividing Powers

Chapter 5-1 Exponents.

Lesson 7-1 Multiplying Monomials

Multiplication Properties of Exponents

Multiplying monomials with monomial

Multiplying and Factoring

Multiplication Properties of Exponents

Dividing Monomials.

Radicals Simplifying.

ALGEBRA what you need to know..

– 3.4 ANSWER 3.5 ANSWER 1.17.

Combine Like Terms Notes Page 23

Presentation transcript:

Chapter 8.1

 Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems  Students will know how to apply the laws of exponents when multiplying monomials.

 Example 1-  Simplify: x 2 * x 3  Remember: x 2 = x * x which can also be written as xx  x 2 = x * x and x 3 = x * x * x  Therefore x 2 * x 3 = (x*x)*(x*x*x) = xx * xxx = xxxxx  There are 5 x’s in the answer  Therefore x 2 * x 3 = x 5  Rule: When multiplying monomials you must add the exponents together. X m * x n = x m+n

* x 3 * x 4 3. x 5 (x 3 ) 4. x 7 (x -2 )

* x 3 * x 4 3. x 5 (x 3 ) 4. x 7 (x -2 ) 3737 x7x7 x8x8 x5x5

 Example 2-  Simplify (2x 3 )(3x 4 )  Multiply the numbers together first: 2 * 3 = 6  Multiply the variables together second: x 3 * x 4 = x 7  Put the numbers and letters back together for your answer: 6x 7  Rule: When multiplying monomials you multiply the numbers and letter separately

1. 3x 3 * 4x x 4 (2x 3 ) 3. -2x 2 (4x) 4. -7x(-3x 3 )

1. 3x 3 * 4x x 4 (2x 3 ) 3. -2x 2 (4x) 4. -7x(-3x 3 ) 12x 5 10x 7 -8x 3 21x 4

 Example 3-  Simplify (-2x 2 y 3 )(3x 5 y 2 )  Multiply the numbers together first: –2 * 3 = -6  Multiply the x’s separately: x 2 * x 5 = x 7  Multiply the y’s separately: y 3 * y 2 = y 5

1. 3x 3 y 2 * 4x 2 y x 4 y 3 (2x 3 y 4 ) 3. -2x 2 y 2 (4xy) 4. -7xy(-3x 3 y 3 ) 12x 5 y 4 10x 7 y 7 -8x 3 y 3 21x 4 y 4

 Example 4  Simplify (x 3 ) 2  Remember, (x 3 ) 2 = (x 3 ) * (x 3 ) = xxx * xxx  Therefore (x 3 ) 2 = x 6  Rule: When a monomial with an exponent is then raised to an exponent you multiply the exponents together. (X m ) n = x m*n  You can always write out x 3 twice and add the exponents

1. (x 2 ) 3 2. (x 4 ) 4 3. (x 3 ) 7

1. (x 2 ) 3 2. (x 4 ) 4 3. (x 3 ) 7 x6x6 x 16 x 21

 Example 5  Simplify: 2x 2 (3x 3 ) 2  Remember order of operations, exponents come before multiplication!  Also, any number squared means to multiply it by itself  Therefore: 2x 2 (3x 3 )(3x 3 )  Multiply the numbers: 2 * 3 * 3 = 18  Multiply the variables: x 2 * x 3 * x 3 = x 8  Put the numbers and letters back together: 18x 8

1. 2x 2 (3x 3 ) 2 2. (4x 3 ) 2 (2x 5 ) 3. (3x 4 ) 3 (2x 3 ) 2

1. 2x 2 (3x 3 ) 2 2. (4x 3 ) 2 (2x 5 ) 3. (3x 4 ) 3 (2x 3 ) 2 18x 8 108x 18 32x 11

1. x 2 * x x(2x 3 ) 3. -2x 3 (4x 4 ) 4. (x 4 ) x 3 (3x 4 ) 2

1. x 2 * x x(2x 3 ) 3. -2x 3 (4x 4 ) 4. (x 4 ) x 3 (3x 4 ) 2 x5x5 6x 4 x 12 -8x 7 18x 11