Objective 123 Multiplying binomials by trinomials ©2002 by R. Villar All Rights Reserved.

Slides:

Advertisements

Similar presentations

Objective Factor quadratic trinomials of the form x2 + bx + c.

Advertisements

2-5 Example 2 Find the product of 87 and 39. Use the traditional multiplication method. 1. Estimate. 90 × 40 = 3,600 Lesson 4-13 Example 2.

Lesson 4-8 Example Find the product of 231 and 7. Estimate first. Step 1 Estimate. 200 × 7 = 1,400.

4.5 Multiplying Polynomials

Multiplication of Polynomials.  Use the Distributive Property when indicated.  Remember: when multiplying 2 powers that have like bases, we ADD their.

Special Products of Polynomials.

Section 9-3 Multiplying Binomials SPI 12D: multiply two polynomials with each factor having no more than two terms Objectives: Multiply binomials by modeling.

8.3 Multiplying Binomials

Warm Up 1.) What is the simplified form of –x2(2x3 + 5x2 + 6x)?

Converting Quadratic Equations A step-by-step guide with practice.

 We use the acronym below to multiply two binomials. F – O – I – L – FIRST OUTSIDE INSIDE LAST.

5.3 Add, Subtract, and Multiply Polynomials. Add Polynomials Vertically or Horizontally Find the sum of the polynomials below: 2x 3 – 5x + 3x – 9 and.

5.3Product of Two Binomials. Remember! Powers/Exponents: Distributing:

6.3 Adding, Subtracting, & Multiplying Polynomials p. 338.

Degree The largest exponent Standard Form Descending order according to exponents.

Multiplication: Special Cases Chapter 4.5. Sum x Difference = Difference of Two Squares (a + b)(a – b) = (a – b)(a + b) =a 2 – b 2.

Multiplying Polynomials

9.3 Multiplying Binomials. 9.3 – Mult. Binomials Goals / “I can…”  Multiply binomials using FOIL  Multiply trinomials by binomials.

5.4 Multiplying Polynomials

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

Aim: How do we multiply polynomials? Do Now: Multiply the following 1. 2x(3x + 1) 2. (x – 1)(x + 2) 3. (x +2)(x 2 – 3x + 1)

Lesson 7-7 Multiplying Polynomials

AIM: What method can we use to multiply a trinomial by a binomial?

Day Problems Simplify each product. 1. 8m(m + 6) 2. -2x(6x3 – x2 + 5x)

Multiplying Binomials Mentally (the FOIL method) Chapter 5.4.

M ULTIPLYING P OLYNOMIALS : FOIL Lesson M ULTIPLYING P OLYNOMIALS When multiplying two BINOMIALS… …we multiply by “FOIL” First terms Outer terms.

I. Using the Distributive Property To simplify a of two binomials, you can each term of the first binomial to each term in the binomial. PRODUCT DISTRIBUTE.

Multiplying Polynomials January 29, Page #10-38 even 10) terms: 5x 3, x; coefficients: 5, 1 12) term: 7x 2 ; coeff: 7 14) monomial 16) monomial.

2.2 Warm Up Find the sum or difference. 1. (2x – 3 + 8x²) + (5x + 3 – 8x²) 2. (x³ - 5x² - 4x) – (4x³ - 3x² + 2x – 8) 3. (x – 4) – (5x³ - 2x² + 3x – 11)

Unit 8, Lesson 7a. (x+3)(x+2) Multiplying Binomials (FOIL) FOIL = x 2 + 2x + 3x + 6 = x 2 + 5x + 6.

Multiply two binomials using FOIL method

5.9 Multiplication of Monomials and Binomials Goals: 1.To multiply a monomial and a poly 2.To multiply 2 binomials (FOIL)

1.(-7) (-2) 2.(3)(-6) 3.(4)(5) 4.(-3) (4t) 5.(2)(-2x) 6.(7y)(3) 7.3(s+5) 8.4(-n+2) 9.4-(t+2) 10.3n+(2-n)

Multiplying Polynomials January 29, Page #10-38 even 10) terms: 5x 3, x; coefficients: 5, 1 12) term: 7x 2 ; coeff: 7 14) monomial 16) monomial.

EXAMPLE 3 Multiply polynomials vertically

Binomial X Binomial The problems will look like this: (x – 4)(x + 9)

8.3 Multiplying Binomials Objective: to multiply two binomials or a binomial by a trinomial.

8.7 Multiplying Polynomials What you’ll learn: 1.To multiply two binomials 2.To multiply two polynomials.

Polynomials Objective: To review operations involving polynomials.

Section 5.4 Factoring Quadratic Expressions Obj: to find common and binomial factors of quadratic expressions.

Algebra 2a September 13, 2007 Chapter Five review.

1.(-7) (-2) 2.(3)(-6) 3.(4)(5) 4.(-3) (4t) 5.(2)(-2x) 6.(7y)(3) 7.3(s+5) 8.4(-n+2) 9.4-(t+2) 10.3n+(2-n) Algebra S9 Day 21.

EXAMPLE 3 Multiply polynomials vertically Find the product (b 2 + 6b – 7)(3b – 4). SOLUTION STEP 1 Multiply by – 4. b 2 + 6b – 7 – 4b 2 – 24b b –

Objective 119 Multiplying 2 binomials, (x + a)(x + b) ©2002 by R. Villar All Rights Reserved.

Factoring Quadratic Trinomials a = 1 Chapter 10.5.

Lesson 10.2 Multiplying Polynomials Objective: To multiply polynomials Multiply monomials by other polynomials by using distributive property Examples.

Multiplication of Trinomials Elvira Scotto-Padavano Middletown High School.

8.7 Multiplying Polynomials. Multiplying a Binomial by a Binomial A binomial is a polynomial with two terms. To multiply a binomial by a binomial, you.

Multiply two binomials using FOIL method

Section 9.3 – 9.4 Review Algebra I.

Factoring Trinomials.

Multiplication of monomial and binomials.

Polynomials and Polynomial Functions

Multiplying 2 Digit Factors

? 1 ten 1 ten = 10 ones How many ten?

Factoring Trinomials 1 February 1, 2017.

Multiplying Binomials and Special Cases

Multiplying Polynomials

= x2 + 10x + 21 = x2 – 121 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2)

Multiplying Polynomials

EXPONENT RULES Why are they important? Try some:.

Factoring Trinomials.

Objective multiply two polynomials using the FOIL method and the distributive property.

Unit 1 Section 3B: MULTIPLYING POLYNOMIALS

Factoring Trinomials Day #1

(2)(4) + (2)(5) + (3)(4) + (3)(5) =

Multiplying Polynomials

Multiplying Polynomials

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

Multiplication: Special Cases

Presentation transcript:

Objective 123 Multiplying binomials by trinomials ©2002 by R. Villar All Rights Reserved

Multiplying binomials by trinomials To multiply a binomial by a trinomial, we cannot use the FOIL method…it only works for binomials by binomials… Instead, we must distribute... Example: Multiply (x + 4)(x 2 + 4x – 2) Distribute each term of the binomial by the trinomial… (x + 4)(x 2 + 4x – 2) x(x 2 + 4x – 2) + 4(x 2 + 4x – 2) x 3 + 4x 2 – 2x + 4x x – 8 Now, collect like terms... x 3 + 8x x – 8

Example: Multiply (2x – 3)(3x 2 – x + 1) Distribute each term of the binomial by the trinomial… (2x – 3)(3x 2 – x + 1) 2x(3x 2 – x + 1) – 3(3x 2 – x + 1) 6x 3 – 2x 2 + 2x – 9x 2 + 3x – 3 Now, collect like terms... 6x 3 – 11x 2 + 5x – 3

You can also multiply binomials by trinomials vertically... Example: Multiply 2x 2 – x + 5 x – 3 Multiply as if this was a 2 digit multiplication problem... First, multiply the “one’s place (the –3 in this problem)... –6x 2 + 3x – 15 Then, multiply the “ten’s place (the x in this problem)... 2x 3 – x 2 + 5x Now, add like terms (notice that like term are lined up)... 2x 3 – 7x 2 + 8x – 15