Q 28. Expand ax-by4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 28. (page 836)

Expand ${(a x - b y)}^{4}$ using Binomial Theorem

Short Answer

Expert verified

The value of ${(a x - b y)}^{4} = a^{4} x^{4} - 4 a^{3} b x^{3} y + 6 a^{2} b^{2} x^{2} y^{2} - 4 a b^{3} x y^{3} + b^{4} y^{4}$

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

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

$鈬� {(a x - b y)}^{4} = a^{4} x^{4} - 4 a^{3} b x^{3} y + 6 a^{2} b^{2} x^{2} y^{2} - 4 a b^{3} x y^{3} + b^{4} y^{4}$

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Expand ${(a x - b y)}^{4}$ using 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

Calculus

Probability and Statistics

Mechanics Maths

Geometry

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Expand ax-by4using 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

Calculus

Probability and Statistics

Mechanics Maths

Geometry

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Expand ${(a x - b y)}^{4}$ using Binomial Theorem