how can i tell when to use the foil method?

Question

whats the difference between foiling and distributing? 

Answer 1

"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.

 

Answer 2

Try to multiply these six factors to get rid of the parentheses:

f(n) = (4n+3)(4n+2)(4n+1)(4n)(4n-1)(4n-2)

FOIL quickly fails you.

But here’s an example of using the Distributive Property in a methodical way that provides error checking as you go:

http://www.wyzant.com/resources/answers/30917/simplify_the_expression

Answer 3

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