Math Example--Polynomial Concepts--Polynomial Expansion: Example 08

Topic

Polynomials

Description

This example illustrates the expansion of the polynomial expression (x + 1)(x + 3)(x - 12). The solution employs the FOIL method and distribution to expand the expression step-by-step. The final result of this expansion is x³ - 8x² - 45x - 36.

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 examine our eighth example of polynomial expansion. We have the expression (x + 1)(x + 3)(x - 12). Notice that we have both addition and subtraction within the parentheses. As we work through this expansion using the FOIL method and distribution, pay close attention to how the signs change when we multiply positive and negative terms. Can you predict what the coefficient of x^2 will be in the final expression? This example will help you understand how to handle more complex expansions with mixed terms, which is essential for advanced algebraic problem-solving.

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