Multiplying Polynomials

• Monomials.

Procedure: (Multiplying Monomials)

To multiply monomials, multiply the coefficients and then multiply the variables using the product rule for exponents.

• Monomials and polynomials with more than one term.

Procedure: (Multiplying a Monomial by a Polynomial)

Distribute the monomial among the terms of the polynomial, then use the procedure for multiplying monomials.

• Polynomials with more than one term.

• Consider the following example:

Example:

(3x - 1)(2x + 5) (Do this example by distribution.)

• Notice that, once again, we wound up multiplying each term of the first binomial by each term of the second.

Example:

(a ² + a - 5)(2a + 3) (Again, use distribution.)

• Notice that, once again, we wound up multiplying each term of the first polynomial by each term of the second.

Procedure: (Multiplying Any Two Polynomials)

Multiply each term of the first polynomial by each term of the second polynomial and combine like terms.