Technical Mathematics, Sixth Edition

2.7. Multiplying a Multinomial by a Multinomial

We come now to the most general situation, multiplying an expression with any number of terms by another expression having any number of terms.

We multiply multinomials in the same way that we multiplied other expressions. We make use of the distributive law for multiplication and multiply every term in one multinomial by every term in the other. Then combine like terms.

Example 67: Here is a binomial times a trinomial.

Example 68: Here's another similar to Ex. 67.

Example 69: This example shows a binomial times a polynomial with four terms.

To multiply three multinomials, first multiply two of them. Then multiply that product by the third multinomial. This procedure can, of course, be extended to multiply any number of multinomials.

Example 70: Multiply (4 − x)(5 − x)(6 + x). Solution: Let us first multiply one pair of binomials, say, (5 − x)(6 + x) (5 − x)(6 + x) = 30 + 5x − 6x − x2 = 30 − x − x2 Then let us multiply that product by (4 − x).

TI-89 screen for Example 70.

To multiply two multinomials that have three or more ...