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how can i tell when to use the foil method?

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3 Answers

"Foiling" IS distributing.
 
The FOIL method is used to multiply binomials, or to multiply (x + 3) by (3x -12) for example.
 
But FOILing can ONLY be used with binomials.  Let find out why:
 
FOILing means first multiplying the FIRST terms together, or x and 3x to get 3x2
Then multiply the OUTSIDE terms together, or x and -12 to get -12x.
Then multiply the INSIDE terms together, or 3 and 3x to get 9x.
The multiply the LAST terms together, or 3 and -12 to get -36.
Simplify by adding like terms to get 3x2  -3x -36.
 
If we were to use distribution to multiply (x + 3) by (3x -12) we'd multiply x by 3x.
Then multiply x by -12.
Then multiply 3 by 3x.
Then multiply 3 by -12.
 
So FOILing IS distributing, but one cannot use the FOIL method on anything else but binomials.
 
i.e. we can't use the FOIL method to find the product of a trinomial and an binomial.
 
The foil method is best used when the expression is in the form (x+a)*(x+b), where a and b are numbers. In this case, you need to go x*x + xa +xb + ab.
 
Distribution would be when there is only one term in one of the parenthesis, such as in the case of x*(x+3), in which case, it would be x*x + x*3.

(x+4)(x-3) = x^2 + x - 12 << FOIL

x*(x+3) = x^2 + 3x << Distribution

Comments

Your foil one IS distribution.  This gives the impression that foil is something besides distribution.
I just avoid FOIL all together, it is just useless memorization of irrelevance:
 
 Multiply 2 binomial
 
   ( X + a ) ( X +b)
 
    Just distribute it twice:
    
   ( X +a) X + b( X +a) = X ^2 + aX + bX + ab
 
      Then factor by Grouping:
 
         X^2 + ( a + b ) X + ab
       
      Then it comes useful in factoring Quadratic and solving for roots
 
  f( X) =  X ^2 + ( a + b ) X + ab = ( X +a ) ( X +b )  
     
     f( x ) = 0   ( X +a ) = 0   X1 = -a     ( X +b) = 0   X2 = -b
 
         Substituting back ( X, X2 ) into f( X)
 
      f( X) = X^2 - ( X1 + X 2 ) X + X1X2     (2)
 
     Equation (2) leads  us to solution of roots of quadratic.
 
          Where aX^2 + bX + c = 0
 
                   always   X1 + X2 = - b/a   X1 . X2= c/a (3)
 
            Relationship ( 3) is the key Principle that leads to the solution of quadratic and even polynomial'
 
            that should be emphasized instead of FOIL.