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Math Example--Polynomial Concepts--Polynomial Expansion: Example 04

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# Math Example--Polynomial Concepts--Polynomial Expansion: Example 04

## Topic

Polynomials

## Description

This example illustrates the expansion of the polynomial expression x(x - 9)(x - 7). The solution is presented step-by-step, demonstrating how to expand the expression one pair of terms at a time. The final result of this expansion is x^{3} - 16x^{2} + 63x.

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 examine our fourth example of polynomial expansion. We have the expression x(x - 9)(x - 7). Notice that both terms in parentheses are subtractions. How do you think this will affect our final result? As we work through this expansion, pay close attention to how the signs change when we multiply negative terms. Can you predict the signs of the terms 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.__

Common Core Standards | CCSS.MATH.CONTENT.HSA.APR.A.1, CCSS.MATH.CONTENT.HSA.APR.B.2, CCSS.MATH.CONTENT.HSA.APR.C.5, CCSS.MATH.CONTENT.HSA.APR.C.4, CCSS.MATH.CONTENT.HSA.APR.B.3 |
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Grade Range | 9 - 12 |

Curriculum Nodes |
Algebra• Polynomials• Polynomial Expressions |

Copyright Year | 2013 |

Keywords | polynomials, expansion |