Study Guide: Multiplying Polynomials

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Study Guide
Multiplying Polynomials

The following examples show how the distributive property and collecting like terms can be used to multiply any two polynomials.

Example 1 illustrates the use of the F O I L method - first, outer, inner, last. This method is usually employed when the problem is presented as the product of two "horizontal" binomials.
Example 2 shows that polynomials can be multiplied vertically.

Directions: Find each product.

1. (5t + 4)(2t − 6)

2. (5m − 3n)(4m − 2n)

3. (a − b)(2a − 5b)

10t² − 22t − 24

20m² − 22mn + 6n²

2a² − 11ab + 15b²

4. (3x − 0.1)(x + 0.1)

**5. (8x + 5)(8x − 5)

6. (x + 5)(x + 2)

3x² + 0.2x − 0.01

64x² − 25

x² + 7x + 10

7. (2x − 4)(2x + 5)

4x² + 2x − 20

2y⁴ − 3y³ − 33y² + 41y − 12

6b⁴ − 13b³ + 8b² − 3b

**Problem 5 is a special type of product. It is called the difference in perfect squares. The general form of this type of problem is (a + b)(a − b) = a² − b². Take a moment to go back and examine your calculations for this problem. You will note that the "outer" and "inner" products cancelled.

Another special type of product is when you are asked to square a binomial. The general forms for this type of product are:

(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²