Area Models with Polynomials

Topic

Polynomials.

Definition

An area model with polynomials is a visual representation used to illustrate the multiplication of polynomial expressions. It breaks down the polynomials into their constituent terms and arranges them in a grid format to show how each term interacts with others.

Description

Area models are a powerful tool in the study of polynomials, particularly in understanding the multiplication process. By using a grid to represent the terms of the polynomials, students can visually see how each term in one polynomial multiplies with each term in another polynomial. This method not only aids in comprehension but also helps in organizing the multiplication process systematically.

For example, consider the multiplication of two binomials, such as (x + 2) and (x + 3). An area model would place x and 2 along one axis and x and 3 along the other. The intersections within the grid would represent the products of these terms: x • x, x • 3, 2• x, and 2 • 3. Summing these products gives the expanded form of the polynomial: $$x^2 + 5x + 6$$

This visual approach is particularly useful for students who struggle with abstract algebraic manipulations, as it provides a concrete method to understand polynomial multiplication. It also lays a foundation for more advanced topics in algebra, such as factoring polynomials and solving polynomial equations.

For a complete collection of terms related to polynomials click on this link: Polynomials Collection.