Warm-Up 5 minutes Multiply. 1) (x – 3)(x – 2) 2) (6x + 5)(2x + 1)

Slides:

Advertisements

Similar presentations

Homework for 9-3 p , 5, 8, 10, 12, 15, 16, 20, 24, 28, 30, 33, 36, 40, 43, 50, 53.

Advertisements

Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. SOLUTION 3y 2 (y – 2) + 5(2 – y) b. 2x(x + 4) – 3(x + 4) = (x + 4)(2x – 3) a. The binomials.

Math 025 Section 10.1 Radicals. Perfect square Square root 1  1 = 1 4  4 = 2 9  9 = 3 16  16 = 4 25  25 = 5 36  36 = 6 49  49 = 7 64  64 = 8 81.

WU #19 Simplify: 4x2 – 2x x2 + 4x – 1 Multiply: (x + 7)(x – 2)

7.1 – Multiplying Monomials. x · x = x 1 · x 1 =

6 – 4: Factoring and Solving Polynomial Equations (Day 1)

4.6 Special Products. Objective 1 Square binomials. Slide

8.5 – Factoring Differences of Squares. Recall: Recall: Product of a Sum & a Difference.

Warm Up Simplify (–2) (x)2 5. –(5y2) x2 –5y2

Special Products of Binomials

Several Methods 1.Trial and Error – More mental math 2.Grouping – Longer method FACTORING TRINOMIALS WITH LEADING COEFFICIENT > 1.

Polynomials and Factoring Review By: Ms. Williams.

Special Products of Binomials

Polynomials P4.

Polynomials. The Degree of ax n If a does not equal 0, the degree of ax n is n. The degree of a nonzero constant is 0. The constant 0 has no defined degree.

4.6 Multiplying Polynomials. Objectives  Multiply two or more monomials  Multiply a polynomial and a monomial  Multiply a binomials by a binomial.

Multiplying Binomials Objectives: To Multiply Two Binomials FOIL To multiply the sum and difference of two expressions To square a binomial.

EXAMPLE 3 Multiply polynomials vertically and horizontally a. Multiply – 2y 2 + 3y – 6 and y – 2 in a vertical format. b. Multiply x + 3 and 3x 2 – 2x.

7.6 Factoring Differences of Squares CORD Math Mrs. Spitz Fall 2006.

Multiplying Polynomials *You must know how to multiply before you can factor!”

Algebra 10.3 Special Products of Polynomials. Multiply. We can find a shortcut. (x + y) (x – y) x² - xy + - y2y2 = x² - y 2 Shortcut: Square the first.

Multiplying Special Cases

2.3Special Products of Polynomials Square of a Binomial Pattern Multiply binomials by using F O I L.

Multiplication of Exponential Expressions with the Same Base Evaluate each expression, and compare the results obtained in the first column with the corresponding.

Special Products of Binomials

Special Products of Binomials

Aim: How do we factor polynomials completely? Do Now: Factor the following 1. 2x 3 y 2 – 4x 2 y 3 2. x 2 – 5x – 6 3. x 3 – 5x 2 – 6x.

SECONDARY ONE 6.1a Using Substitution to Solve a System.

9.1 – Multiplying & Dividing Rational Expressions.

Factor out a common binomial

Notes 8.4 – MULTIPLYING SPECIAL CASES

7-1 Integer Exponents 7-2 Powers of 10 and Scientific Notation 7-3 Multiplication Properties of Exponents 7-4 Division Properties of Exponents 7-5 Fractional.

Math Pacing Special Products 3 5 3x – 5 6x + 3. Special Products 8-7 Multiplying Polynomials.

Objective: To multiply binomials using Area Model.

Quiz Use Synthetic Substitution to evaluate: 3.What is the “end behavior” for: 2. Simplify When x = 2 In other words:

EXAMPLE 3 Multiply polynomials vertically and horizontally a. Multiply –2y 2 + 3y – 6 and y – 2 in a vertical format. b. Multiply x + 3 and 3x 2 – 2x +

5.3C- Special Patterns for Multiplying Binomials SUM AND DIFFERENCE (a+b)(a-b) = a² - b² (x +2)(x – 2) = x² -4 “O & I” cancel out of FOIL SQUARE OF A BINOMIAL.

9.7 MULTIPLYING POLYNOMIALS

Warm Up 1.) What is the factored form of 2x2 + 9x + 10? 2.) What is the factored form of 6x2 – 23x – 4?

Warm Up Factor each expression. 1. 3x – 6y 3(x – 2y) 2. a2 – b2

Warm-Up Perform the given operation: 1. (-6x3 + 5x2 – 5) + (12x2 + 11)

Special Products of Polynomials

8.6 Choosing a Factoring Method

7.6 Factoring Differences of Squares

Multiplying Binomials and Special Cases

Factor. x2 – 10x x2 – 16x + 1 Multiply. 3. (4x- 3y)(3x +4y)

BELL-WORK (x – 5)(x + 5) = x2 – 25 (b) (3x – 2)(3x + 2) = 9x2 – 4

Notes Over 10.3 Multiply binomials by using F O I L.

Factoring Special Cases

Warm-up: Write in scientific notation: ,490,000

Difference of Two Squares

Multiplying Special Cases

I can use the generic rectangle to simplify expressions.

Warm-Up Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Factoring Special Cases

Factoring Special Cases

Warm Up: Solve the Equation 4x2 + 8x – 32 = 0.

FACTORING SUMS and DIFFERENCES of CUBES

Objective Factor polynomials by using the greatest common factor.

(B12) Multiplying Polynomials

Objective Find special products of binomials..

Objective Factor polynomials by using the greatest common factor.

X values y values. x values y values Domain Range.

Review Multiply (3b – 2)(2b – 3) Multiply (4t + 3)(4t + 3)

Algebra 1 Section 9.5.

7.3 Special Products.

8-7 Factoring Special Cases

Warm-Up 5 minutes Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

5.10 Multiplying Binomials: Special Products

Warm Up Simplify: 5(b+4) 2)-3(2x+5) 3)4(-8-3q) 4)- 6(2b-7)

Presentation transcript:

Warm-Up 5 minutes Multiply. 1) (x – 3)(x – 2) 2) (6x + 5)(2x + 1) 3) (2xy + 4x)(-2y + y2)

8.4 Multiplying Binomials – Special Products Objectives: To multiply the sum and difference of two expressions To square a binomial

Example 1 Multiply. (x + 6)(x – 6) = (x)(x) + (x)(-6) + (6)(x) + (6)(-6) = x2 – 6x + 6x - 36 = x2 - 36

Example 2 Multiply. (2x + 4)(2x – 4) = (2x)(2x) + (2x)(-4) + (4)(2x) + (4)(-4) = 4x2 – 8x + 8x - 16 = 4x2 - 16

Example 3 Multiply. (-3x + 4y)(-3x – 4y) = (-3x)(-3x) + (-3x)(-4y) + (4y)(-3x) + (4y)(-4y) = 9x2 + 12xy – 12xy – 16y2 = 9x2 – 16y2

Example 4 Multiply. (x + 2)2 = (x + 2)(x + 2) = (x)(x) + (x)(2) + (2)(x) + (2)(2) = x2 + 2x + 2x + 4 = x2 + 4x + 4

Example 5 Multiply. (x - 3)2 = (x - 3)(x - 3) = (x)(x) + (x)(-3) + (-3)(x) + (-3)(-3) = x2 - 3x - 3x + 9 = x2 - 6x + 9

Example 6 Multiply. (2x – 3y)2 = (2x – 3y)(2x – 3y) = (2x)(2x) + (2x)(-3y) + (-3y)(2x) + (-3y)(-3y) = 4x2 - 6xy - 6xy + 9y2 = 4x2 - 12xy + 9y2

Example 7 812 = (80 + 1)2 = 802 + 2(80 • 1) + 12 Square the binomial. Multiplying Special Cases Example 7 4 a. Find 812 using mental math. 812 = (80 + 1)2 = 802 + 2(80 • 1) + 12 Square the binomial. = 6400 + 160 + 1 = 6561 Simplify. b. Find 592 using mental math. 592 = (60 – 1)2 = 602 – 2(60 • 1) + 12 Square the binomial. = 3600 – 120 + 1 = 3481 Simplify. Quick Check

Multiplying Special Cases Example 8 Ex. Find 43 • 37. 43 • 37 = (40 + 3)(40 – 3) Express each factor using 40 and 3. = 402 – 32 Find the difference of squares. = 1600 – 9 = 1591 Simplify.