Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

1:49 minutes

Problem 42b

Textbook Question

In Exercises 39–48, factor the difference of two squares. 64x^2−81

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Difference of Squares

The difference of squares is a specific algebraic identity that states that the difference between two squared terms can be factored into the product of their sum and difference. The general form is a^2 - b^2 = (a + b)(a - b). This concept is essential for simplifying expressions and solving equations involving squared terms.

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In the context of polynomials, factoring helps in simplifying expressions and solving equations. Understanding how to factor different types of polynomials, including the difference of squares, is a fundamental skill in algebra.

Quadratic Expressions

Quadratic expressions are polynomial expressions of degree two, typically in the form ax^2 + bx + c. In the case of the difference of squares, we specifically deal with expressions that can be rewritten as the difference between two squared terms. Recognizing and manipulating quadratic expressions is crucial for solving various algebraic problems, including factoring.