/*! 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 53 Find each product. $$(2 x+3)^{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 53

Find each product. $$(2 x+3)^{3}$$

Short Answer

Expert verified
The product of `(2x + 3)^3` is `8x^3 + 36x^2 + 54x + 27`.

Step by step solution

01

Identify the Components

In our case, we can identify `a` as `2x` and `b` as `3`. We are given that `n` is `3` as the power of the binomial. Now we substitute our identified values into the binomial theorem.
02

Substitute into the Binomial Theorem

Substituting these values into the binomial theorem gives us: `(2x)^3 + (C(3, 1) * (2x)^2 * 3) + (C(3, 2) * (2x) * 3^2) + 3^3`. Here, `(2x)^3` implies cube of 2x, `C(3, 1)` stands for the number of ways to select one element from three, similarly, `C(3, 2)` stands for the number of ways to select two elements from three.
03

Compute the Binomial Coefficients

First, calculate the binomial coefficients. `C(3, 1)` is `3` and `C(3, 2)` is also `3`.
04

Simplify

Now we simplify the entire expression, yielding `8x^3 + 36x^2 + 54x + 27`.

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

Describe what it means to rationalize a denominator. Use both \(\frac{1}{\sqrt{5}}\) and \(\frac{1}{5+\sqrt{5}}\) in your explanation.

Evaluate each exponential expression in $$\frac{x^{14}}{x^{-7}}$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$ \frac{1}{2}+\frac{2}{3} $$

Describe what it means to raise a number to a power. In your description, include a discussion of the difference between \(-5^{2}\) and \((-5)^{2}\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.