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Multiplying Monomials and/or Binomials and FOIL  Concept
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Multiplying rational expressions is basically two simplifying problems put together. When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel. Dividing rational expressions is the same as multiplying with one additional step: we take the reciprocal of the second fraction and change the division to multiplication.
One of the most common problem types you're going to see in your study of polynomials is going to ask you to multiply either binomials, trinomials, monomials stuff like that, so before we get into binomials let's talk about monomials. The way you work with monomials is using the same processes you would use for distributing. You take that monomial and you multiply it by everything in the other term in the another polynomial you're multiplying by it's like distributing.
When you come to binomials it's tricky because it's like double distributing, so if the double distributing makes sense you could do it that way, or lot of people use this acronym FOIL to help them with multiplying two binomials.
FOIL is an acronym for how to multiply binomials, first of all acronym means the letters stand for processes each letter in the word FOIL stands for some process we're going to do. Find the products of the first terms that's what f is, outers, inner terms and last terms and write them as a polynomial, that's what FOIL stands for it only works for product of binomials meaning you're multiplying two things that have two terms each that's when you'll use the FOIL process, so you could do this also somewhere you guys you're going to see the area model for multiplying polynomials and we'll get into that during other videos but FOIL is what I really want you guys to remember is pretty commonly used but just please please please only use FOIL when multiplying two binomials.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”
Sample Problems (6)
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Multiplying Monomials and/or Binomials and FOIL
Problem 1 9,483 viewsMultiply:
a) (3x²)(5x⁴)b) (⅓x²y)(12xy²)c) 5x(3x² − 2y − 4) 
Multiplying Monomials and/or Binomials and FOIL
Problem 2 8,421 viewsMultiply:
(3x + 1)(x + 4) 
Multiplying Monomials and/or Binomials and FOIL
Problem 3 945 views 
Multiplying Monomials and/or Binomials and FOIL
Problem 4 882 views 
Multiplying Monomials and/or Binomials and FOIL
Problem 5 947 views 
Multiplying Monomials and/or Binomials and FOIL
Problem 6 848 views
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