Chapter 12: Q. 216E (page 1213)

In the following exercises, expand each binomial.
$(a + b)^{6}$

Short Answer

Expert verified

Expansion is $a^{6} + 6 a^{5} b + 15 a^{4} b^{2} + 20 a^{3} b^{3} + 15 a^{2} b^{4} + 6 a b^{5} + b^{6}$

Step by step solution

Step 1. Given Information

Expand $(a + b)^{6}$

Step 2. Solution

We have

$(a + b)^{6} = (\begin{matrix} 6 \\ 0 \end{matrix}) a^{6 - 0} b^{6 - 6} + (\begin{matrix} 6 \\ 1 \end{matrix}) a^{6 - 1} b^{6 - 5} + (\begin{matrix} 6 \\ 2 \end{matrix}) a^{6 - 2} b^{6 - 4} + (\begin{matrix} 6 \\ 3 \end{matrix}) a^{6 - 3} b^{6 - 3} + (\begin{matrix} 6 \\ 4 \end{matrix}) a^{6 - 4} b^{6 - 2} + (\begin{matrix} 6 \\ 5 \end{matrix}) a^{6 - 5} b^{6 - 1} + (\begin{matrix} 6 \\ 6 \end{matrix}) a^{6 - 6} b^{6 - 0} = a^{6} + 6 a^{5} b + 15 a^{4} b^{2} + 20 a^{3} b^{3} + 15 a^{2} b^{4} + 6 a b^{5} + b^{6}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, expand each binomial.
$(a + b)^{6}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Discrete Mathematics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, expand each binomial.(a+b)6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Discrete Mathematics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, expand each binomial.
$(a + b)^{6}$