/*! 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 51 Find each product. $$(x+1)^{3}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 51

Find each product. $$(x+1)^{3}$$

Short Answer

Expert verified
The cubic of the expression \( (x+1) \) is \( x^{3} + 3x^{2} + 3x + 1 \).

Step by step solution

01

Write Binomial Expression

Write down the binomial expression whose cube needs to be found. This is the expression: \((x+1)^{3}\).
02

Apply Binomial Theorem

Apply the binomial theorem, \( (a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k} \), where \( n = 3 \), \( a = x \), \( b = 1 \), and \( \binom{n}{k} \) is the binomial coefficient: \((x+1)^{3} = \binom{3}{0}x^{3}1^{0} + \binom{3}{1}x^{2}1^{1} + \binom{3}{2}x^{1}1^{2} + \binom{3}{3}x^{0}1^{3}\) .
03

Calculate Binomial Coefficients

For binomial coefficient, calculate as: \(\binom{n}{m} = \frac{n!}{m!(n-m)!}\), so, \(\binom{3}{0} = 1, \binom{3}{1} = 3, \binom{3}{2} = 3, \binom{3}{3} = 1 \). Replace these values.
04

Simplify the Expression

On substituting the calculated coefficients and simplifying, we obtain: \(x^{3} + 3x^{2} + 3x + 1\).

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

Simplify using properties of exponents. $$\left(125 x^{9} y^{6}\right)^{3}$$

Explain the quotient rule for exponents. Use \(\frac{5^{8}}{5^{2}}\) in your explanation.

Evaluate each expression without using a calculator. $$8^{\frac{2}{3}}$$

Explain how to simplify \(\sqrt{10} \cdot \sqrt{5}\)

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

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.