/*! 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} Q. 401 In the following exercises, fact... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 401 (page 636)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.

a3鈭�125

Short Answer

Expert verified

The Factored form of given polynomial is,

(a-5)a2+5a+25

Step by step solution

01

Step 1. Given Information 

We are given a polynomial,

a3鈭�125

The formula used for factoring using sum and difference of cube is ,

(a3-b3)=(a-b)(a2+ab+b2)(a3+b3)=(a+b)(a2-ab+b2)

02

Step 2. Factorizing the polynomial

The given polynomial can be written as,

a3鈭�125=a3鈭�53

Using (a3-b3)=(a-b)(a2+ab+b2), we get

role="math" localid="1644740536630" a3鈭�125=(a-5)a2+a.5+52a3鈭�125=(a-5)a2+5a+25

03

Step 3. Checking the factorization by multiplying 

Multiplying the factors, we get

(a-5)a2+5a+25=a3鈭�125a3+5a2+25a-5a2-25a-125=a3鈭�125a3鈭�125=a3鈭�125LHS=RHS

Hence the factorization is correct.

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

Factor completely using trial and error:4b2+5b+1
In the following exercises, factor.

x3+x2鈭�x鈭�1.

Find the greatest common factors: 14x3,70x2,105x.

In the following exercises, factor completely.

48q3-24q2+3q

How do you recognize the binomial squares pattern?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

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.