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 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+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. (3x 2 +1)(2x 2 _ 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. (3x 2 +1)(2x 2 _ 2) 1.Multiply 3*2=6 2.Carry x=x 3.Add Exponents=4 Front=6x 4

7. 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

8. 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

9. 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

10. 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