Question

Use Pascals Triangle to expand each binomial. $$(a+b)^{7}$$

   Use Pascals Triangle to expand each binomial.
$$(a+b)^{7}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 22

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

Step 1

The 7th row of Pascal's Triangle is 1, 7, 21, 35, 35, 21, 7, 1. Show more…

Show all steps

lock

Thanks for your feedback!

Use Pascals Triangle to expand each binomial. $$(a+b)^{7}$$

Play audio

Feedback

Powered by NumerAI

Amy Jiang and 99 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Pascal's Triangle

Pascal's Triangle is a triangular array of numbers where each number is the sum of the two directly above it. It is used to find the coefficients in the expansion of a binomial expression, with each row corresponding to the power of the binomial, making it a quick and efficient way to determine the coefficients in terms like (a+b)^n.

Binomial Theorem

The Binomial Theorem provides a formula to expand expressions of the form (a+b)^n. It states that the expansion is the sum of terms given by the binomial coefficients multiplied by the appropriate powers of the two terms, expressed in the form ? [n choose k] a^(n-k) b^k, where k ranges from 0 to n.

Binomial Coefficients

Binomial coefficients, represented as C(n, k) or 'n choose k', indicate the number of ways to choose k elements from a set of n elements. These coefficients are found in Pascal's Triangle and are essential in determining the weight of each term in the binomial expansion according to the Binomial Theorem.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later