Q 17. Expand x+15聽using the Binomial ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 17. (page 836)

Expand ${(x + 1)}^{5}$ using the Binomial Theorem

Short Answer

Expert verified

The value of ${(x + 1)}^{5} = x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1$

Step by step solution

Step 1. Defination

Let $x$ and $a$ be real numbers. For any positive integer $n$ , we have ${(x + a)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) x^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a x^{n - 1} + 鈰� 鈰� + (\begin{matrix} n \\ j \end{matrix}) a^{j} x^{n - j} + 鈰� 鈰� + (\begin{matrix} n \\ n \end{matrix}) a^{n} = {鈭�}_{j = 0}^{n} (\begin{matrix} n \\ j \end{matrix}) x^{n - j} a^{j}$

Step 2. Explanation

$鈬� {(x + 1)}^{5} = (\begin{matrix} 5 \\ 0 \end{matrix}) {(1)}^{0} {(x)}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(1)}^{1} {(x)}^{4} + (\begin{matrix} 5 \\ 2 \end{matrix}) {(1)}^{2} {(x)}^{3} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(1)}^{3} {(x)}^{2} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(1)}^{4} {(x)}^{1} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(1)}^{5} {(x)}^{0}$

$鈬� {(x + 1)}^{5} = \frac{5!}{0! (5 - 0)!} x^{5} + \frac{5!}{1! (5 - 1)!} x^{4} + \frac{5!}{2! (5 - 2)!} x^{3} + \frac{5!}{3! (5 - 3)!} x^{2} + \frac{5!}{4! (5 - 4)!} x + \frac{5!}{5! (5 - 5)!}$

鈬� {(x + 1)}^{5} = x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1

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91影视

Expand ${(x + 1)}^{5}$ using the Binomial Theorem

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

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91影视

Expand x+15using the Binomial Theorem

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Mechanics Maths

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Expand ${(x + 1)}^{5}$ using the Binomial Theorem