Math Example--Polynomial Concepts--Polynomial Expansion: Example 11

Topic

Polynomials

Description

This example demonstrates the expansion of the polynomial expression (x + 9)(x - 7)(x - 6). The solution utilizes the FOIL method and distribution to expand the expression step-by-step. The final result of this expansion is x³ - 4x² - 75x + 378.

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

The importance of multiple worked-out examples in understanding 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: Now, let's look at our eleventh example of polynomial expansion. We have the expression (x + 9)(x - 7)(x - 6). Notice that we have one addition and two subtractions within the parentheses. As we expand this expression using FOIL and distribution, pay close attention to how the signs change when we multiply positive and negative terms. Can you predict the sign of the x² term in our final expression? Remember, understanding the pattern of signs in polynomial expansion is crucial for solving more complex problems in algebra.

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