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Explanation of Multiplying Binomial Expressions - Succeed in Algebra. Also refer to monomial, term, FOIL method, factoring, trinomial, quadratic, mathematics, math, maths, Ron Kurtus, School for Champions. Copyright © Restrictions Multiplying Binomial Expressionsby Ron Kurtus (3 April 2008) A binomial is an expression consisting of two terms or monomials separated by a plus (+) or minus (−) sign. Examples of binomials include ax + b, x2 − y2 and 2x + 3y. Even x + 2 + 7 is a binomial, since it reduces to x + 9, which has two terms. Multiplying two binomial expressions can be similar to multiplication of numbers. Typically, the FOIL method is used to multiply binomials. Multiplying binomial expressions is often used to verify the factoring of a trinomial or quadratic expression. Questions you may have are:
This lesson will answer those questions. There is a mini-quiz near the end of the lesson. Similar to multiplying numbersMultiplying binomials is similar to multiplying two 2-digit numbers. Suppose you wanted to multiply 21 × 32. You could write the multiplication as:
Break into binomial formAnother perspective on it is break the numbers into a form similar to a binomial:
Note: I hope it lined up on your computer. Multiply two binomialsNow, you can use the same method to multiply two binomials together:
Breaking it down that multiplication, step-by-step is:
FOIL methodSince binomials are simple and you are smart, a FOIL method is usually used to multiply two binomials. FOIL stands for multiply the First terms, multiply the Outside terms, multiply the Inside terms and multiply the Last terms. To multiply (ax + b)(cx + d), you follow the procedure:
Typically, you can do these operations in your head, writing down the results in their order. ExampleMultiply (x + 3y)(2x − 5y)
Write down: 2x2
Add − 5xy: 2x2 − 5xy
Add 6xy: 2x2 − 5xy + 6xy = 2x2 + xy
Add −15y2 for final result: 2x2 + xy − 15y2 Special formAnother example is: (2x + 3y)(2x − 3y) =
Note: When you multiply binomials in the form of (ax + by)(ax − by), the result is a2x2 − b2y2. Remember this shortcut, because it will come up time and time again in Algebra. (x − 2)(x + 2) = x2 − 4 When binomials not similarWhen the binomials are not similar, it can get tricky:
ExercisesTry the following exercises: 1. (5x − 7)(x + 2) 2. (x2 + 3)(x2 + 3) 3. (x − y)(3x − 2y) 4. (4 − y)(y + 4) 5. (a + b)(c + d) Answers1. 5x2 + 3x − 14 2. x4 + 6x2 + 9 3. 3x2 − 5y + 2y2 4. y2 − 16 5. ac + ad + bc + bd SummaryMultiplying two binomial expressions can be similar to multiplication of numbers. Typically, the FOIL (First, Outside, Inside, Last) method is used to multiply binomials. Multiplying binomial expressions is often used to verify the factoring of a trinomial or quadratic expression. Use clever tools to make work easier ResourcesThe following resources provide information on this subject: WebsitesBooksMiscellaneousMini-quiz to check your understanding1. Is 5 + 4x − 3 a binomial? 2. What is (x + 3)2 equal to? 3. What is the product of (5x − 7)(x + 2)? If you got all three correct, you are on your way to becoming a Champion in Algebra. If you had problems, you had better look over the material again. What do you think?Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible. Share linkFeel free to establish a link from your website to pages in this site. Or use our form to send this link to yourself or a friend. Students and researchersThe Web address of this page is Please include it as a reference in your report, document, or thesis. Where can you go from here?
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