Math Example--Polynomial Concepts--Polynomial Expansion: Example 05

Topic

Polynomials

Description

This example demonstrates the expansion of the polynomial expression (x + 2)(x + 3)(x + 4). The solution utilizes the FOIL method and distribution to expand the expression step-by-step. The final result of this expansion is x³ + 9x² + 26x + 24.

Polynomial expansion is a fundamental concept in algebra that involves multiplying polynomial expressions. This collection of examples serves as an excellent teaching tool by presenting various scenarios of polynomial expansion. By working through these examples, students can develop a deeper understanding of the expansion process and learn to apply it to different types of expressions.

The importance of multiple worked-out examples in mastering polynomial expansion cannot be overstated. Each example in this collection presents a unique combination of terms, allowing students to recognize patterns and differences in the expansion process. This repetition helps reinforce the underlying principles and builds students' confidence in their ability to expand polynomials independently.

Teacher's Script: Let's look at our fifth example of polynomial expansion. We have the expression (x + 2)(x + 3)(x + 4). Notice that all terms in parentheses are additions this time. As we work through this expansion using the FOIL method and distribution, pay attention to how the constant terms combine. Can you predict what the degree of the final polynomial will be? Remember, when we multiply polynomials, the degrees add. This example will help you understand how to handle expansions with multiple positive terms.

For a complete collection of math examples related to Polynomials click on this link: Math Examples: Polynomial Expansion Collection.