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)

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