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.
Find (2m - 5)(m + 4) using the FOIL method.
Find (2k - 5)
(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