Special Products
 The socalled FOIL method of multiplying
two binomials is nothing more than a special case of
multiplying polynomials. The acronynm FOIL stands for First,
Outside, Inside, and Last.
 When multiplying the sum and difference of two terms, the
FOIL method leads to the two middle terms cancelling
out.}
Example:
Use FOIL to multiply (2x + 3)(2x  3)
Shortcut (Product of the Sum and the Difference of Two
Terms)
( A + B )( A  B) = A^{ 2}  B^{ 2}.
Any binomial in the form A^{ 2} is called a difference
of squares .
 When squaring a binomial, one must remember to FOIL and NOT
JUST SQUARE EACH TERM .
Example:
Compute (5a  2)^{ 2}
Shortcut (Squaring a Binomial)
( A + B )^{ 2} = A^{ 2} + 2AB + B^{ 2}
( A  B )^{ 2} = A^{ 2}  2AB + B^{ 2}
 None of the formulae in this section are strictly
needed to succeed in algebra. They are shortcuts, and
nothing else. You will not be tested on them, but they
can save you a lot of time if you know how to use them
properly.
