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Why not use FOIL?

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  • soorlsn
    In Algebra 1 why is FOIL not taught for factoring polynomials? My son couldn t understand all the arrows going every which way, but his sister who is in
    Message 1 of 2 , Jan 12, 2012
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      In Algebra 1 why is FOIL not taught for factoring polynomials? My son couldn't understand all the arrows going every which way, but his sister who is in college Algebra 2 showed him FOIL.
      I know it isn't in the text, but do you use it when you teach?
      Or, is there some reason it shouldn't be used?
    • 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 2 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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