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Re: Why not use FOIL?

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  • David Chandler
    FOIL (which stands for First, Outer, Inner, Last) is a memory trick that is limited to multiplying two binomials: (a + b)(c + d) = ac + ad + bc + bd. There is
    Message 1 of 2 , Jan 12, 2012
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      FOIL (which stands for First, Outer, Inner, Last) is a memory trick
      that is limited to multiplying two binomials:
      (a + b)(c + d) = ac + ad + bc + bd.
      There is nothing wrong with reciting "first, outer, inner, last", as
      far as it goes, but it does not extend to larger problems. For
      instance, try
      (a + b)(c + d + e) = ___.
      If you rely on FOIL as a memory trick you're stuck. If, however, you
      remember that each term in the first group gets multiplied by each
      term in the second group, this is just about as easy as before:
      (a + b)(c + d + e) = ac + ad + ae + bc + bd + be.
      Just put your left finger on "a" and cycle through the three terms on
      the right. Then put your left finger on "b" and cycle through them
      again. Now try this:
      (a + b + c)(d + e + f) = ___.
      Follow the same principle.

      I tell my students about the FOIL method, because some already know
      it, but I then show them the general pattern (an extension of the
      distributive law), which I recommend as better in the long run.
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