
A binomial is a polynomial with exactly two terms, such as 2x
+ 1 or m + n. When two binomials are multiplied, the FOIL method
(First, Outer, Inner, Last) is used as a memory aid.
EXAMPLE
Find (2m  5)(m + 4) using the FOIL method.
Solution
EXAMPLE
Find (2k  5)
Solution
Use FOIL.
(2k  5) = (2k  5)(2k  5)
= 4k 10k  10k + 25
= 4k  20k + 25
Notice that the product of the square of a binomial is the
square of the first term (2k), plus twice the product of the two terms,
(2)(2k)(5), plus the square of the last term (5) .
CAUTION Avoid the common error of writing (x
+ y) = x + y. As Example 5 shows, the square of a binomial has
three terms, so
(x + y) = x + 2xy + y
Furthermore, higher powers of a binomial also result in more
than two terms. For example, verify by multiplication that
(x + y) = x + 3xy + 3xy + y
Remember, for any value of n1
