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The FOIL Method

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)

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The FOIL Method

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

  2. 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 7x2 or -10 • A binomial is just 2 monomials. Ex. (5x2 +5) • Trinomial is 3 monomials. Ex. (5x2 +10x-1) {When you multiply 2 binomials, you will always get a trinomial. • Polynomial is a name for 4 or more monomials. Ex. (10x3+5x2+8x+9+10+3+7)

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

  4. How To Use The FOIL Method • First, you need to have 2 binomials to be able to use the FOIL method. (3x2+1)(2x2 _2)

  5. 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}

  6. Front • Front means that you will take the front numbers of the binomials and multiply them together. (3x2+1)(2x2 _2) Multiply 3*2=6 Carry x=x Add Exponents=4 Front=6x4

  7. Front=6x4 Outer • Outer means that you will take the outer two numbers of the binomials and multiply them together. (3x2+1)(2x2 _2) Multiply 3*-2=-6 Carry x=x Add Exponents=2 Outer=-6x2

  8. Front=6x4 Outer=-6x2 Inner • Inner means that you will take the inner two numbers of the binomials and multiply them together. (3x2+1)(2x2 _2) Multiply 1*2=2 Carry x=x Add Exponents=2 Inner=2x2

  9. Front=6x4 Outer=-6x2 Inner=2x2 Last • Last means that you will take the last two numbers of the binomials and multiply them together. (3x2+1)(2x2 _2) Multiply 1*-2=-2 Carry x=N/A Add Exponents=N/A Last=-2

  10. FINAL STEP! • The final step of the FOIL method is to simplify! (3x2+1)(2x2 _2) These numbers have the same exponent value, so they can be added together as like terms. Front=6x4 Outer=-6x2 Inner=2x2 Last=-2 -4x2 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: 6x4-4x2-2

  11. Any Questions?

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