Math Example--Polynomial Concepts--Polynomial Expansion: Example 03

Topic

Polynomials

Description

This example demonstrates the expansion of the polynomial expression x(x + 5)(x - 8). The solution is presented step-by-step, showing how to expand the expression one pair of terms at a time. The final result of this expansion is x³ - 3x² - 40x.

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 third example of polynomial expansion. We have the expression x(x + 5)(x - 8). Notice how we have both addition and subtraction within the parentheses, similar to our previous example. As we expand this expression step by step, pay close attention to how the signs change when we multiply positive and negative terms. Can you predict what the sign of the last term in our final expression will be? Remember, understanding how signs work in multiplication is crucial for correctly expanding polynomials.

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