/*! 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 35 Find each product. $$(5-7 x)(5... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 35

Find each product. $$(5-7 x)(5+7 x)$$

Short Answer

Expert verified
The product of \((5-7x)(5+7x)\) is \(25 - 49x^2\).

Step by step solution

01

First terms multiplication

Multiply the first terms in each bracket. The first terms are \(5\) and \(5\). Thus, \(5 * 5 = 25\).
02

Outer terms multiplication

Next, multiply the outer terms found in the brackets. Here, the outer terms are \(5\) and \(-7x\), so the multiplication gives \(-35x\).
03

Inner terms multiplication

Now, multiply the inner terms. In this case, the inner terms are \(-7x\) and \(5\). The product is \(-35x\).
04

Last terms multiplication

Multiply the last terms in each bracket. Under consideration are \(-7x\) and \(7x\), and their multiplication gives \(-49x^2\).
05

Summing Up

Sum up the results from the individual steps. \(25 - 35x - 35x - 49x^2\) simplifies to \(25 - 70x - 49x^2\). However, because of a little trick in mathematics called 'difference of squares', where \(a^2 - b^2 = (a - b)(a + b)\), the final result is \(25 - 49x^2\). This is because the middle term which consists of \(x\) will cancel out each other.

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

Perform the indicated operations. $$(x-y)^{-1}+(x-y)^{-2}$$

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.

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 more U.S. marriages, spouses have different faiths. The bar graph shows the percentage of households with an interfaith marriage in 1988 and \(2012 .\) Also shown is the percentage of households in which a person of faith is married to someone with no religion. The formula $$ I=\frac{1}{4} x+26 $$ models the percentage of U.S. households with an interfaith marriage, \(I, x\) years after \(1988 .\) The formula $$ N=\frac{1}{4} x+6 $$ models the percentage of U.S households in which a person of faith is married to someone with no religion, \(N, x\) years after \(1988 .\) Use these models to solve Exercises \(107-108\). The formula for converting Celsius temperature, \(C,\) to Fahrenheit temperature, \(F\), is $$ F=\frac{9}{5} C+32 $$ If Fahrenheit temperature ranges from \(41^{\circ}\) to \(50^{\circ},\) inclusive, what is the range for Celsius temperature? Use interval notation to express this range.

This will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$2(x-3)-17=13-3(x+2)$$ is the resulting statement true or false?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and 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.