Math Example--Polynomial Concepts--Difference of Squares and Cubes--Example 8

Topic

Polynomials

Description

This example shows how to factor x² - 81, applying the difference of squares twice, first on x² - 81, then on the resulting expression.

In this example, students explore the difference of squares or cubes, helping them recognize patterns in algebraic expressions that can simplify factorization. For quadratic expressions like x² - n, recognizing these as differences of squares allows students to factor them into two binomials. For higher degree expressions, similar methods apply, enabling the application of systematic factorization techniques.

Seeing multiple worked-out examples is crucial for students as it helps reinforce pattern recognition, deepens understanding, and builds confidence in solving such problems independently. By examining various instances, students gain familiarity with different forms and degrees of expressions, enabling them to adapt the approach to similar problems.

Teacher’s Script: Let's go over this example together. Here, we have the expression The expression x⁴ - 81 is factored as (x² - 9)(x² + 9), then further factored as (x - 3)(x + 3)(x² + 9). Our goal is to recognize it as a difference of squares or cubes and apply the factorization techniques we've learned. Pay close attention to each step, as understanding this process will help you tackle similar problems on your own.

For a complete collection of math examples related to Difference of Squares and Cubes click on this link: Math Examples: Difference of Squares and Cubes Collection.