/*! 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 52 Find the indicated term of each ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 52

Find the indicated term of each binomial expansion. \((y+4)^{7} ;\) fifth term

Short Answer

Expert verified
The fifth term of the binomial expansion \((y+4)^7\) is \(\boxed{8960y^3}\).

Step by step solution

01

Identify the binomial terms and the term index

From the given expression, we identify: - \(a = y\) - \(b = 4\) - \(n = 7\) - \(k = 4\)
02

Use the binomial theorem formula

Now plug the values of \(a\), \(b\), \(n\), and \(k\) into the binomial theorem formula: \[\binom{n}{k}a^{n-k}b^k = \binom{7}{4}y^{7-4}4^4\]
03

Calculate the binomial coefficient

Calculate the binomial coefficient using the formula \(\binom{n}{k} = \frac{n!}{k!(n-k)!}\): \[\binom{7}{4} = \frac{7!}{4!(3)!} = \frac{7\times6\times5}{4\times3\times2} = 35\]
04

Calculate the y exponent

Subtract \(k\) from \(n\): \[7 - 4 = 3\]
05

Calculate the power of 4

Calculate \(4^4\): \[4^4 = 256\]
06

Combine the results

Now, combine the results of Step 3, Step 4, and Step 5: \[35 \cdot y^3 \cdot 256\] So, the fifth term of the binomial expansion \((y+4)^7\) is \(\boxed{8960y^3}\).

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

Evaluate each binomial coefficient. $$\left(\begin{array}{l}9 \\\3\end{array}\right)$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$a_{1}=20, r=-\frac{3}{4}$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$\frac{7}{2}, \frac{7}{4}, \frac{7}{8}, \frac{7}{16}, \dots$$

Use the formula for \(S_{n}\) to find the sum of the terms of each geometric sequence. $$\sum_{i=1}^{4} 10\left(-\frac{2}{5}\right)^{i}$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$-12,8,-\frac{16}{3}, \frac{32}{9}, \dots$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.