The FOIL Method Brandon Cohen Northwest Rankin Middle School Science Bowl Team Alumni.

Slides:



Advertisements
Similar presentations
Vocabulary Lesson 10.1 Algebra Objective: I will be able to identify a polynomial and determine its degree.
Advertisements

Factoring Polynomials.
When you are multiplying two binomials use FOIL. FOIL stands for First Outer Inner Last When you multiply two binomials you generally end up with three.
5.2 Multiplying Polynomials. To Multiply Polynomials Each term of one polynomial must be multiply each term of the other polynomial.
Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 + 7y – 8y 2 – 1 ANSWER 2y 2 + 7y – 1.
4.5 Multiplying Polynomials
Multiplying Polynomials
Chapter 9 Polynomials and Factoring A monomial is an expression that contains numbers and/or variables joined by multiplication (no addition or subtraction.
Exponents and Polynomials
Polynomials Algebra I.
Polynomials and Factoring
FACTORING An ALGEBRAIC Adventure FACTORING An ALGEBRAIC Adventure Don’t be a scaredy CAT.
Polynomials P4.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.
7.6 Polynomials and Factoring Part 1: Polynomials.
Degree The largest exponent Standard Form Descending order according to exponents.
How do you perform operations with polynomials? Section P4 (old text)
5-2 Polynomials Objectives Students will be able to: 1)Add and subtract polynomials 2)Multiply polynomials.
 Simplify the following…  2(4 + x)  x(x – 3x 2 + 2)  5x – 2 + 6x  2x 2 + 5x – 11x  8x(4x 2 )
Multiplying Polynomials
Warm-up Answer the following questions 1.Did you have a good night? 2.What 2 numbers multiplied together = 30 AND if added, together = 11? 3.Fill in the.
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
Slide 7- 1 Copyright © 2012 Pearson Education, Inc.
Day Problems Simplify each product. 1. 8m(m + 6) 2. -2x(6x3 – x2 + 5x)
CLASSIFYING POLYNOMIALS. A _______________ is a sum or difference of terms. Polynomials have special names based on their _______ and the number of _______.
Multiplying Polynomials. Exponents Remember if you are multiplying numbers with the same base, then ADD the exponents together. Examples:
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 1.
Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 1 Exponents and Polynomials 5.
Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:
Understanding Polynomials
6.1 Review of the Rules for Exponents
9-2 Multiplying and Factoring
Multiplying by a Monomial Be able to multiply two monomials or a monomial and a polynomial.
Polynomials Lesson 5.2: Adding, Subtracting, and Multiplying Polynomials By: Just Just Leininger Period 3 modern algebra.
Multiplying Polynomials with FOIL Objective: Students will multiply two binomials using the FOIL method. S. Calahan March 2008.
8.7 Multiplying Polynomials What you’ll learn: 1.To multiply two binomials 2.To multiply two polynomials.
Factoring a polynomial means expressing it as a product of other polynomials.
Adding and Subtracting Polynomials. 1. Determine whether the given expression is a monomial (Yes or No). For those that are monomials, state the coefficient.
Name ____________________________________________ Date _______________ Per_____ Polynomials Review Adding Ex: 1. Simplify 2. Find the perimeter Subtracting.
Operations and equations
Terms Monomials separated by addition or subtraction signs Polynomials A monomial or the sum of monomials Binomial---2 terms Trinomial---3 terms Monomial---1.
 Adding and Subtracting Polynomials. What is a monomial? Give an example. 1.
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.
Multiplying Binomials
Polynomials and Polynomial Functions
Polynomials and Polynomial Functions
Objective - To multiply polynomials.
Polynomials and Polynomial Functions
Polynomial Equations and Factoring
Algebra I Section 9.1 – 9.2 Review
Dividing Polynomials.
Multiplying Polynomials
13 Exponents and Polynomials.
Naming Polynomials Add and Subtract Polynomials Multiply Polynomials
Factoring Polynomials.
= x2 + 10x + 21 = x2 – 121 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2)
Multiply polynomials When multiplying powers with the same base, keep the base and add the exponents. x2  x3 = x2+3 = x5 Example 1: Multiplying Monomials.
Adding and subtracting
Multiplying Polynomials
Polynomials A polynomial is a sum of monomials. Common polynomials:
How do you multiply polynomials?
Dividing Polynomials.
Factoring Trinomials Day #1
8-3 Multiplying Polynomials by Using FOIL
Ch Part 1 Multiplying Polynomials
8-1: Adding & Subtracting Polynomials
Learning Target: I will be able to identify polynomials
Multiplying Polynomials
Presentation transcript:

The FOIL Method Brandon Cohen Northwest Rankin Middle School Science Bowl Team Alumni

Quick Terminology A monomial is just a single variable that can be with a number and be to a power or just a single number. Ex. 5x or 7x 2 or -10 A binomial is just 2 monomials. Ex. (5x 2 +5) Trinomial is 3 monomials. Ex. (5x 2 +10x-1) {When you multiply 2 binomials, you will always get a trinomial. Polynomial is a name for 4 or more monomials. Ex. (10x 3 +5x 2 +8x )

What Is The FOIL Method? The FOIL method is one way to multiply binomials. FOIL stands for Front, Outer, Inner, Last

How To Use The FOIL Method First, you need to have 2 binomials to be able to use the FOIL method. (3x 2 +1)(2x 2 _ 2)

Instructions On each step, you need to multiply the numbers {No number=We infer it equals 1} If there is an “x” or another variable, they will just carry over. Then add the exponents together for same variables. {If no number over variables only!=we infer it is to the 1 power}

Front Front means that you will take the front numbers of the binomials and multiply them together. (3x 2 +1)(2x 2 _ 2) 1.Multiply 3*2=6 2.Carry x=x 3.Add Exponents=4 Front=6x 4

Outer Outer means that you will take the outer two numbers of the binomials and multiply them together. (3x 2 +1)(2x 2 _ 2) Front=6x 4 1.Multiply 3*-2=- 6 2.Carry x=x 3.Add Exponents=2 Outer=-6x 2

Inner Inner means that you will take the inner two numbers of the binomials and multiply them together. (3x 2 +1)(2x 2 _ 2) 1.Multiply 1*2=2 2.Carry x=x 3.Add Exponents=2 Inner=2x 2 Front=6x 4 Outer=-6x 2

Last Last means that you will take the last two numbers of the binomials and multiply them together. (3x 2 +1)(2x 2 _ 2) 1.Multiply 1*-2=-2 2.Carry x=N/A 3.Add Exponents=N/A Last=-2 Front=6x 4 Outer=-6x 2 Inner=2x 2

FINAL STEP! The final step of the FOIL method is to simplify! (3x 2 +1)(2x 2 _ 2) Front=6x 4 Outer=-6x 2 Inner=2x 2 Last=-2 These numbers have the same exponent value, so they can be added together as like terms. -4x 2 Typically, when you add like terms and simplify the individual parts into one trinomial, you do it in order of greatest to least of the EXPONENT. Answer: 6x 4 -4x 2 -2