/*! 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 100 Explain how to find the product ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 100

Explain how to find the product of the sum and difference of two terms. Give an example with your explanation.

Short Answer

Expert verified
The product of the sum and difference of two numbers is equal to the difference of their squares, as shown with \( a = 5 \) and \( b = 3 \): \( 16 = 16 \)

Step by step solution

01

Understand the formula

Before calculating anything, it is important to understand the formula \( a^2 - b^2 = (a + b)(a - b) \). It states that the difference of the squares of two numbers \( a \) and \( b \) is equal to the product of the sum \( (a + b) \) and the difference \( (a - b) \) of the same two numbers.
02

Choose two numbers

To illustrate this, choose two specific numbers for \( a \) and \( b \). For this example, let's take \( a = 5 \) and \( b = 3 \). These values are chosen arbitrarily; the formula will hold for any two numbers.
03

Calculate the squares

Calculate the squares of the chosen numbers. In this case, \( a^2 = 5^2 = 25 \) and \( b^2 = 3^2 = 9 \). Then subtract \( b^2 \) from \( a^2 \) to get the difference of the squares, \( 25 - 9 = 16 \)
04

Calculate sum and difference

Now calculate the sum and difference of the chosen numbers, \( a + b = 5 + 3 = 8 \) and \( a - b = 5 - 3 = 2 \). Then multiply these results together to get \( 8 * 2 = 16 \)
05

Compare the results

Finally, compare the results from steps 3 and 4. If the formula is correct, both calculations should have the same result. In this case, \( 16 = 16 \), as expected, so the formula \( a^2 - b^2 = (a + b)(a - b) \) is verified for \( a = 5 \) and \( b = 3 \)

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

What is the discriminant and what information does it provide about a quadratic equation?

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\sqrt{20}}{8}=\frac{\sqrt{10}}{4}$$

Each group member should research one situation that provides two different pricing options. These can involve areas such as public transportation options (with or without discount passes), cellphone plans, long-distance telephone plans, or anything of interest. Be sure to bring in all the details for each option. At a second group meeting, select the two pricing situations that are most interesting and relevant. Using each situation, write a word problem about selecting the better of the two options. The word problem should be one that can be solved using a linear inequality. The group should turn in the two problems and their solutions.

In solving \(\sqrt{2 x-1}+2=x,\) why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{-1}-(y+2)^{-1}}{2}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

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.