Q. 12.72. Use the Binomial Theorem to expa... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.72. (page 1210)

Use the Binomial Theorem to expand ${(y - 1)}^{6}$ .

Short Answer

Expert verified

The expansion of the given binomial is, $y^{6} - 6 y^{5} + 15 y^{4} - 20 y^{3} + 15 y^{2} - 6 y + 1$

Step by step solution

Step 1. Given information.

The given expression is, ${(y - 1)}^{6}$

Step 2. Substitute the values and simplify.

Substitute in the values into the binomial expansion,

$a = y b = - 1 n = 6$

Now

${(y - 1)}^{6} = (\begin{matrix} 6 \\ 0 \end{matrix}) y^{6} + (\begin{matrix} 6 \\ 1 \end{matrix}) y^{6 - 1} (- 1) + (\begin{matrix} 6 \\ 2 \end{matrix}) y^{6 - 2} {(- 1)}^{2} + (\begin{matrix} 6 \\ 3 \end{matrix}) y^{6 - 3} {(- 1)}^{3} + (\begin{matrix} 6 \\ 4 \end{matrix}) y^{6 - 4} {(- 1)}^{4} + (\begin{matrix} 6 \\ 5 \end{matrix}) y^{6 - 5} {(- 1)}^{5} + (\begin{matrix} 6 \\ 6 \end{matrix}) {(- 1)}^{6}$

Simplify the exponents.

${(y - 1)}^{6} = (\begin{matrix} 6 \\ 0 \end{matrix}) y^{6} - (\begin{matrix} 6 \\ 1 \end{matrix}) y^{5} + (\begin{matrix} 6 \\ 2 \end{matrix}) y^{4} - (\begin{matrix} 6 \\ 3 \end{matrix}) y^{3} + (\begin{matrix} 6 \\ 4 \end{matrix}) y^{2} - (\begin{matrix} 6 \\ 5 \end{matrix}) y + (\begin{matrix} 6 \\ 6 \end{matrix})$

Evaluate the coefficients. Remember,

$(\begin{matrix} n \\ 1 \end{matrix}) = n, (\begin{matrix} n \\ n \end{matrix}) = 1, (\begin{matrix} n \\ 0 \end{matrix}) = 1$

Simplify the exponents,

${(y - 1)}^{6} = 1 y^{6} - 6 y^{5} + \frac{6!}{2! 4!} y^{4} - \frac{6!}{3! 3!} y^{3} + \frac{6!}{4! 2!} y^{2} - \frac{6!}{5! 1!} y + 1$

Step 3. Conclusion.

Therefore, the expansion of the given expression is ${(y - 1)}^{6} = y^{6} - 6 y^{5} + 15 y^{4} - 20 y^{3} + 15 y^{2} - 6 y + 1$

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

Use the Binomial Theorem to expand ${(y - 1)}^{6}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values and simplify.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

91影视

Use the Binomial Theorem to expandy-16.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values and simplify.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Use the Binomial Theorem to expand ${(y - 1)}^{6}$ .