whats the difference between foiling and distributing?

"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 3x

^{2}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 3x

^{2 }-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.

## Comments

_{1}= -a ( X +b) = 0 X_{2}= -b_{1 }, X_{2 ) into f( X)}_{1 }+ X_{2 ) X + X}_{1X2 }(2)_{1}+ X_{2 = - b/a }X_{1 }. X_{2= c/a}(3)