/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 126 Explain how to factor the differ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 126

Explain how to factor the difference of two squares. Provide an example with your explanation.

Short Answer

Expert verified
The difference of two squares, \(a^2 - b^2\), can be factored into \((a-b)*(a+b)\). For example, in the equation \(x^2 - 4\), \(a = x\) and \(b = 2\). So, \(x^2 - 4\) factors into \((x - 2)*(x + 2)\).

Step by step solution

01

Recognize the Difference of Two Squares

A difference of two squares is an algebraic equation that takes the form \(a^2 - b^2\). This equation is a 'difference' because of the subtraction involved, and each term is a 'square' because each can be written as something squared.
02

Apply the Factoring Formula

The difference of squares factoring formula is \((a + b)*(a - b)\), where \(a^2\) and \(b^2\) are the squares in the equation to be factored. The equation does not change if the order of the terms in each binomial is reversed.
03

Example application

For example, take the equation \(x^2 - 4\). In this instance, \(a = x\) and \(b = 2\). Replacing \(a\) and \(b\) in the formula gives: \(x^2 - 4\) equals \((x - 2)*(x + 2)\). Thus, \(x^2 - 4\) has been factored into \((x - 2)*(x + 2)\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I prefer interval notation over set-builder notation because it takes less space to write solution sets.

What's wrong with this argument? Suppose \(x\) and \(y\) represent two real numbers, where \(x>y .\) $$\begin{aligned} &2>1\\\ &2(y-x)>1(y-x)\\\ &2 y-2 x>y-x\\\ &\begin{aligned} y-2 x &>-x \\ y &>x \end{aligned} \end{aligned}$$ The final inequality, \(y>x,\) is impossible because we were initially given \(x>y\)

Describe the solution set of \(|x|>-4\)

How is the quadratic formula derived?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2 x-1}{x-7}+\frac{3 x-1}{x-7}-\frac{5 x-2}{x-7}=0$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.