Math Example--Polynomial Concepts--Polynomial Expansion: Example 12

Topic

Polynomials

Description

This example illustrates the expansion of the polynomial expression (x - 1)(x - 10)(x - 8). The solution employs the FOIL method and distribution to expand the expression step-by-step. The final result of this expansion is x³ - 19x² + 98x - 80.

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 twelfth example of polynomial expansion. We have the expression (x - 1)(x - 10)(x - 8). Notice that all terms in parentheses are subtractions this time. As we work through this expansion using the FOIL method and distribution, pay close attention to how the signs change when we multiply negative terms. Can you predict what the sign of the constant term will be in the final expression? This example will help you understand how to handle expansions with multiple negative terms, which is essential for more advanced algebraic manipulations.

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