/*! 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 26 Use the Binomial Theorem to expa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 26

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (x-2)^{5} $$

Short Answer

Expert verified
The expanded form of \( (x-2)^5 \) is \( x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32 \)

Step by step solution

01

Write out the Binomial Theorem

The general form of the binomial theorem is : \[ (a+b)^n = a^n + {n\choose1}a^{n-1}b + {n\choose2}a^{n-2}b^2 + ... + b^n \]. For this problem we have \(a = x\), \(b = -2\), and \(n = 5\).
02

Apply the theorem

Substitute \(a = x\), \(b = -2\), and \(n = 5\) into the binomial theorem: \[ (x - 2)^5 = x^5 + {5\choose1}x^{5-1}(-2) + {5\choose2}x^{5-2}(-2)^2 + {5\choose3}x^{5-3}(-2)^3 + {5\choose4}x^{5-4}(-2)^4 + (-2)^5 \]. Remembering there can be negativity due to negative sign.
03

Substitute and simplify terms

Substitute based on the binomial coefficient: \[ (x - 2)^5 = x^5 - 5x^4*2 + 10x^3*4 - 10x^2*8 + 5x*16 - 32 \]. Simplify the equation by multiplying: \[ (x - 2)^5 = x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32 \]

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

You are dealt one card from a standard 52-card deck. Find the probability of being dealt $$\text{a diamond.}$$

In Exercises \(99-100,\) use a graphing utility to graph the function. Determine the horizontal asymptote for the graph of fand discuss its relationship to the sum of the given series. Function Series $$ f(x)=\frac{2\left[1-\left(\frac{1}{3}\right)^{x}\right]}{1-\frac{1}{3}} \quad 2+2\left(\frac{1}{3}\right)+2\left(\frac{1}{3}\right)^{2}+2\left(\frac{1}{3}\right)^{3}+\cdots $$

Use this information to solve Exercises \(47-48 .\) The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male.

Explaining the Concepts Explain how to find and probabilities with independent events. Give an example.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sequence for the number of seats per row in our movie theater as the rows move toward the back is arithmetic with \(d=1\) so people don't block the view of those in the row behind them.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Mechanics 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.