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What's the Grid Method of FOILing?

Using the Grid Method to FOIL

Summary

  1. The grid method is another method for multiplying two binomials
  2. 4x+2 and 2x-3 are binomials
  3. Set up a tic-tac-toe board, putting the terms of each binomial on the outside
  4. Multiply each pair of terms together, putting the result in the square between them
  5. Write down the terms you got when you multiplied
  6. Simplify by combining like terms, -12x+4x=8x

Notes

    1. The grid method is another way we can multiply two binomials instead of FOILing
    1. This is the example we used when we learned the FOIL method
    2. To see how to multiply this example using FOIL, click the "What is FOIL?" link below
    1. Draw out a grid with three rows and three columns
    1. The first binomial is 4x+2
    2. Put the first term, 4x, in the second box in the left column
    3. Put the second term, 2, in the third box in the left column
    1. The second binomial is 2x-3
    1. The second binomial is 2x-3
    2. Put the first term, 2x, in the second box in the top row
    3. Put the second term, -3, in the third box in the top row
    1. If there is a negative in front of a term, make sure you write that down too
    2. Don't forget the negative sign on the 3!
    1. This will give us the terms for our new polynomial
    1. Multiply the terms on the outside to fill in the box they have in common in the grid
    1. 4x•2x=8x2
    2. 8x2 goes in the box between 4x and 2x
    1. Multiply the terms on the outside to fill in the box they have in common in the grid
    1. 4x•-3=-12x
    2. -12x goes in the box between 4x and -3
    1. 2•2x=4x
    2. 4x goes in the box between 2 and 2x
    1. 2•-3=-6
    2. -6 goes in the box between 2 and -3
    1. The terms we got when we multiplied are the terms of our new polynomial
    2. So we write down 8x2-12x+4x-6
    1. To simplify, we need to combine like terms
    2. -12x and 4x are like terms
    3. Add them together to get -8x
    1. Click on the "What is FOIL?" link below to see how to get this answer using FOIL
    1. We just showed that both methods give us the same answer
    2. So use whichever one you like better!