Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Polynomials Intro

College Algebra

0. Review of Algebra

Polynomials Intro

Previous problemNext problem

2:16 minutes

Problem 71

Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms.(5x + 3)(5x − 3)

Verified step by step guidance

Identify the expression as a product of the sum and difference of two terms: \((a + b)(a - b)\).

Recognize that this expression can be simplified using the difference of squares formula: \((a + b)(a - b) = a^2 - b^2\).

In the given expression \((5x + 3)(5x - 3)\), identify \(a = 5x\) and \(b = 3\).

Apply the difference of squares formula: \((5x)^2 - (3)^2\).

Simplify the expression by calculating \((5x)^2\) and \(3^2\) separately, then subtract the results.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Product of Sum and Difference

The product of the sum and difference of two terms follows the formula (a + b)(a - b) = a² - b². This identity simplifies the multiplication of binomials by eliminating the middle terms, resulting in a difference of squares. In the given expression, a is 5x and b is 3, allowing for straightforward application of this rule.

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which are expressions containing two terms. The process can be executed using the distributive property or special product formulas, such as the one for the product of the sum and difference. Understanding how to manipulate binomials is essential for simplifying algebraic expressions efficiently.

Difference of Squares

The difference of squares is a specific algebraic identity that states a² - b² can be factored into (a + b)(a - b). This concept is crucial when simplifying expressions that fit this form, as it allows for quick calculations and insights into the properties of quadratic expressions. Recognizing this pattern is key to solving problems involving products of binomials.