Q 27. Expand ax+by5聽using Binomial Th... [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 27. (page 836)

Expand ${(a x + b y)}^{5}$ using Binomial Theorem

Short Answer

Expert verified

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

Step by step solution

Step 1. Defination

Let $x$ and $a$ be real number 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

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

$鈬� {(a x + b y)}^{5} = a^{5} x^{5} + 5 a^{4} b x^{4} y + 10 a^{3} b^{2} x^{3} y^{2} + 10 a^{2} b^{3} x^{2} y^{3} + 5 a b^{4} x y^{4} + b^{5} y^{5}$

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91影视

Expand ${(a x + b y)}^{5}$ using Binomial Theorem

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

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91影视

Expand ax+by5using Binomial Theorem

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Expand ${(a x + b y)}^{5}$ using Binomial Theorem