Multiplying Polynomials
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)2
Solution
Use FOIL.
(2k - 5)2 = (2k - 5)(2k - 5)
= 4k2 -10k - 10k + 25
= 4k2 - 20k + 25
Notice that the product of the square of a binomial is the
square of the first term (2k)2, plus twice the product of the two terms,
(2)(2k)(-5), plus the square of the last term (-5)2 .
CAUTION Avoid the common error of writing (x
+ y)2 = x2 + y2. As Example 5 shows, the square of a binomial has
three terms, so
(x + y)2 = x2 + 2xy + y2
Furthermore, higher powers of a binomial also result in more
than two terms. For example, verify by multiplication that
(x + y) = x + 3x2y + 3xy2 + y
Remember, for any value of n ≠ 1
(x + y)n
≠ xn + yn.
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