Question

Use Pascals Triangle to expand each binomial. $$(a+b)^{5}$$

   Use Pascals Triangle to expand each binomial.
$$(a+b)^{5}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 21

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

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The 5th row of Pascal's Triangle is 1, 5, 10, 10, 5, 1. Show more…

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Use Pascals Triangle to expand each binomial. $$(a+b)^{5}$$

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Key Concepts

Binomial Expansion

Binomial Expansion refers to the process of expanding the power of a binomial into a sum of terms, each term being a product of a binomial coefficient and powers of the individual terms of the binomial. This process utilizes the Binomial Theorem and is fundamental to simplifying and evaluating expressions raised to a power.

Combinations

Combinations, often represented as 'n choose k', are mathematical expressions that calculate the number of ways to select k elements from a set of n elements without regard to order. In the context of the Binomial Theorem, these combinations are the coefficients in the expanded form, corresponding to each term in the binomial expansion.

Binomial Theorem

The Binomial Theorem is a formula that provides a method for expanding any power of a binomial expression in the form of (x + y)^n. This theorem shows that each term in the expansion is associated with a specific binomial coefficient, and it provides the general structure of the expanded polynomial.

Pascal's Triangle

Pascal's Triangle is a geometric arrangement of numbers where each number is the sum of the two numbers directly above it. These numbers represent binomial coefficients, which are used in the Binomial Theorem to expand expressions. The triangle provides a quick and visual way to generate these coefficients for any power of a binomial.

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