constant--A term that does not contain a variable.

Slides:



Advertisements
Similar presentations
Name:__________ warm-up 7-1 Use substitution or elimination to solve the system of equations. r – t = –5 r + t = 25 Graph the system of equations. How.
Advertisements

Multiplying and Dividing Monomials. Objectives: Understand the concept of a monomial Use properties of exponents to simplify expressions.
Algebraic Expressions and Formulas
Evaluating Algebraic Expressions
Laws of Exponents: Dividing Monomials Division Rules for Exponents.
Splash Screen. Lesson 1 Menu Five-Minute Check (over Chapter 6) Main Ideas and Vocabulary California Standards Example 1: Identify Monomials Key Concept:
8.1 Multiplying Monomials
Page 370 – Laws of Exponents Multiplying Monomials
Lesson 8-1 Multiplying Monomials. Transparency 1 Click the mouse button or press the Space Bar to display the answers.
Lesson 1 MULTIPLYING MONOMIALS. What are we going to do…  Multiply monomials.  Simplify expressions involving powers of monomials.
Lesson 1 Menu Five-Minute Check (over Chapter 6) Main Ideas and Vocabulary Targeted TEKS Example 1: Identify Monomials Key Concept: Product of Powers Example.
Multiplying and Dividing Monomials 4.3 Monomial: An expression that is either a: (1) numeral or constant, ex : 5 (2)a v ariable, ex: x (3)or a product.
Example 1A LCM of Monomials and Polynomials A. Find the LCM of 15a 2 bc 3, 16b 5 c 2, and 20a 3 c 6. 15a 2 bc 3 = 3 ● 5 ● a 2 ● b ● c 3 Factor the first.
Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Math humor: Question: what has variables with whole-number exponents and a bunch.
Multiply a Polynomial by a Monomial Honors Math – Grade 8.
Use the Distributive Property to: 1) simplify expressions 2) Solve equations.
Simplifying Algebraic Expressions 1-5. Vocabulary Term- a number, a variable, or a product of numbers and variables. Terms in an expression are separated.
Warm-Up #1 11/30 1. Write down these 3 formulas:
Prerequisite Skills VOCABULARY CHECK Copy and complete the statement. ? Terms that have the same variable part are called 1. like terms ANSWER zero ANSWER.
Multiplication Properties of Exponents
Adding and Subtracting Polynomials. 1. Determine whether the given expression is a monomial (Yes or No). For those that are monomials, state the coefficient.
1-6 Simplifying Algebraic Expressions. 1-6 Simplifying Algebraic Expressions In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can.
Splash Screen. Lesson Menu Five-Minute Check (over Chapter 6) CCSS Then/Now New Vocabulary Example 1: Identify Monomials Key Concept: Product of Powers.
Multiplying Monomials (7-1) Objective: Multiply monomials. Simplify expressions involving monomials.
Multiplying Monomials. Monomials A monomial is a number, a variable, or a product of a number and one or more variables. An expression involving the division.
Opener (5 + 6) • 2 a + (b + c) + (d • e) 18k x2 + 5x + 4y + 7
Exponents For all real numbers x and all positive integers m, xm = x x x … x, m factors Evaluate: Answers:
Polynomials Addition and Subtraction of Polynomials.
Algebra Adding and Subtracting Polynomials.
Dividing Monomials.
Distributive Property Multiply and Divide polynomials by a constant worksheet.
7-1 Multiplying Monomials
7-1 Multiplying Monomials
Splash Screen.
WARM-UP PROBLEM Simplify the expression. Assume all variables are positive – 48 ANSWER 3 4.
DO NOW: Simplify. Topic: Algebraic Expressions 2
5.2 Polynomials Objectives: Add and Subtract Polynomials
2/26 Honors Algebra Warm-up
Warm Ups Preview 12-1 Polynomials 12-2 Simplifying Polynomials
Multiplying Monomials
1.4 Basic Rules of Algebra.
Algebraic Expressions 2x + 3y - 7
Section 6.2: Polynomials: Classification, Addition, and Subtraction
Multiplying Monomials
Adding and Subtracting Polynomials
Key Concept: Power of a Power Example 1: Find the Power of a Power
Warm Up Evaluate each expression for y = y + y 2. 7y
Multiplying and Dividing Monomials
6.1 Algebraic Expressions & Formulas
Splash Screen.
Lesson 7-1 Multiplying Monomials
Bell Ringer  .
Key Concept: Power of a Power Example 1: Find the Power of a Power
Splash Screen.
Welcome to Interactive Chalkboard
Splash Screen.
Simplifying Variable Expressions
Dispatch a · a · a · a 2 · 2 · 2 x · x · x · y · y · z · z · z 32x3
Splash Screen.
Indices my dear Watson.
1.2 Distributive Property & Combining Like Terms
Using the Distributive Property to Multiply Monomials and Polynomials
7.1 Multiplying Monomials
7.4 Properties of Exponents
EXAMPLE 1 Use properties of exponents
Do Now: Simplify the algebraic expression 16y6 + 4y4 – 13y
Multiplication properties of Exponents
Division Rules for Exponents
Warm Up Simplify: 5(b+4) 2)-3(2x+5) 3)4(-8-3q) 4)- 6(2b-7)
Presentation transcript:

constant--A term that does not contain a variable. monomial--A number, a variable, or a product of a number and one or more variables. Examples: 3, y, 2x, 5xy2 constant--A term that does not contain a variable. Vocabulary

Answer: Yes; the expression is a constant. Identify Monomials Determine whether each expression is a monomial. Explain your reasoning. A. 17 – c B. 8f 2g C. __ 3 4 D. 5 t Answer: No; the expression involves subtraction, not the product of two variables. Answer: Yes; the expression is the product of a number and two variables. Answer: Yes; the expression is a constant. Answer: No; the expression involves division by a variable. Example 1

A B C D Which expression is a monomial? A. x5 B. 3p – 1 C. D. Example 1

Concept

= –12(r 4+7) Product of Powers A. Simplify (r 4)(–12r 7). (r 4)(–12r 7) = (1)(–12)(r 4)(r 7) Group the coefficients and the variables. = –12(r 4+7) Product of Powers = –12r11 Simplify. Answer: –12r11 Example 2

= 30(c1+5)(d 5+2) Product of Powers B. Simplify (6cd 5)(5c5d2). (6cd 5)(5c5d2) = (6)(5)(c ●c5)(d 5 ● d2) Group the coefficients and the variables. = 30(c1+5)(d 5+2) Product of Powers = 30c6d 7 Simplify. Answer: 30c6d 7 Example 2

A B C D A. Simplify (5x2)(4x3). A. 9x5 B. 20x5 C. 20x6 D. 9x6 Example 2

A B C D B. Simplify 3xy2(–2x2y3). A. 6xy5 B. –6x2y6 C. 1x3y5 D. –6x3y5 Example 2

Concept

[(23)3]2 = (23●3)2 Power of a Power = (29)2 Simplify. = 218 or 262,144 Simplify. Answer: 218 or 262,144 Example 3

Simplify [(42)2]3. A. 47 B. 48 C. 412 D. 410 A B C D Example 3

Concept

GEOMETRY Find the volume of a cube with side length 5xyz. Power of a Product GEOMETRY Find the volume of a cube with side length 5xyz. Volume = s3 Formula for volume of a cube = (5xyz)3 Replace s with 5xyz. = 53x3y3z3 Power of a Product = 125x3y3z3 Simplify. Answer: 125x3y3z3 Example 4

A B C D Express the surface area of the cube as a monomial. A. 8p3q3 B. 24p2q2 C. 6p2q2 D. 8p2q2 A B C D Example 4

Concept

= (8g3h4)4(2gh5)4 Power of a Power Simplify Expressions Simplify [(8g3h4)2]2(2gh5)4. [(8g3h4)2]2(2gh5)4 = (8g3h4)4(2gh5)4 Power of a Power = (84)(g3)4(h4)4 (2)4g4(h5)4 Power of a Product = 4096g12h16(16)g4h20 Power of a Power = 4096(16)g12 ● g4 ● h16 ● h20 Commutative Property = 65,536g16h36 Power of Powers Answer: 65,536g16h36 Example 5

A B C D Simplify [(2c2d3)2]3(3c5d2)3. A. 1728c27d24 B. 6c7d5 C. 24c13d10 D. 5c7d21 A B C D Example 5