Question

Use Pascals Triangle to expand each binomial. $$(x-y)^{7}$$

   Use Pascals Triangle to expand each binomial.
$$(x-y)^{7}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 24

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. $$(x-y)^{7}$$

Play audio

Feedback

Powered by NumerAI

Amy Jiang and 67 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

Sign Handling in Binomial Expansions

When expanding binomials with a subtraction, such as (x - y)^n, careful attention must be paid to the sign of each term. The negative sign attached to one of the variables affects the overall sign of the terms, leading to alternating signs based on the exponent of the negative term.

Pascal's Triangle

Pascal's Triangle is a geometric arrangement of numbers that gives the coefficients needed in the binomial expansion. Each row of the triangle corresponds to the coefficients of (a + b)^n, making it a quick and efficient tool to determine these coefficients.

Binomial Theorem

The Binomial Theorem provides a method to expand expressions of the form (a + b)^n into a sum of terms involving binomial coefficients. It helps in writing the expansion as a sum where each term is of the form coefficient × a^(n-k) × b^k.

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