Question 134867
FOIL stands for First, Outside, Inside, Last.  Used when multiplying two binomials.


For example:  {{{(x+2)(x-1)}}}


The x in the first binomial and the x in the second binomial are FIRST:  {{{(green(x)+2)(green(x)-1)}}}


The x in the first binomial and the -1 in the second are OUTSIDE: {{{(green(x)+2)(x-green(1))}}}


The +2 in the first binomial and the x in the second are INSIDE: {{{(x+green(2))(green(x)-1)}}}



The +2 in the first binomial and the -1 in the second are LAST: {{{(x+green(2))(x-green(1))}}}


Multiply the FIRSTs:  {{{x*x=x^2}}}


Multiply the OUTSIDEs: {{{x*-1=-x}}}


Multiply the INSIDEs: {{{2*x=2x}}}


Multiply the LASTs: {{{2*-1=-2}}}


Add the four products:  {{{x^2-x+2x-2}}}


Collect like terms: {{{x^2+x-2}}}


So:  {{{(x+2)(x-1)=x^2+x-2}}}


You really don't have to do multiplication of binomials in any particular order, but FOIL gives you a systematic approach that ensures that you don't either forget one of the products or duplicate any of the products.  Besides, LIOF doesn't spell anything.


Hope that helps,
John