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How to Accept & Reject Problems Using FOIL

FOIL is a method used to multiply polynomials by each other, ensuring that each term is multiplied by every other term in the problem. A polynomial is an equation with many elements, or terms. FOIL stands for First, Outside, Inside and Last, referring to the order in which you should do your multiplication in the context of the parentheses. Once the equation is solved, you can accept or reject the problem based on the answer.

Things You'll Need

  • Pencil
  • Paper
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Instructions

    • 1

      Write out your values and variables on a piece of paper. Once you know which terms need to be added together before being multiplied, write out your equation. The standard set up is (a+b) x (c+d) = your answer. The multiplication sign between the two parenthetical additions can be omitted as the parentheses next to each other indicates multiplication, such as (a+b)(c+d).

    • 2

      Multiply the first set of variables, denoted by the "F" in FOIL. The first terms are the first two variables in each set of parentheses. Using the previous example, you would multiply "a" and "c" together. Write the result, "ac," on the opposite side of the equal sign. Each term multiplied by another is added together on the other side of the equation.

    • 3

      Multiply the Outside, Inside and Last variables in the sets of parentheses. The inside variables are "b" and "c." The outside variables are "a" and "d," and the last terms are "b" and "d." The goal is to make sure all terms are multiplied by each other and added together on the opposite side of the equal sign. The equation should now read (a+b)(c+d) = ac+ad+bc+bd.

    • 4

      Plug in your known values for their corresponding variables as given in your math problem. You should have an answer that will help you accept or reject your problem. For example, if the problem is about distance and the answer needs to be at least 8 miles for the problem to make sense and you arrive at an answer of 6 miles, you can reject the problem and conclude that the situation described in the problem is not feasible.

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