Binomial Theorem Quiz

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Questions and Answers

How can the polynomial (x + y)^n be expanded according to the binomial theorem?

  • As a product of x and y only
  • As a single term involving the sum of x and y
  • As a sum involving terms of the form ax^by^c (correct)
  • As a sum involving terms of the form ax/y

What does the binomial theorem describe in elementary algebra?

  • The factorization of binomial expressions
  • The simplification of binomial fractions
  • The multiplication of two binomials
  • The algebraic expansion of powers of a binomial (correct)

What are the exponents b and c required to satisfy in the expansion of (x + y)^n?

  • b + c = n (correct)
  • b - c = n
  • b / c = n
  • b * c = n

What do the coefficients in the expansion of (x + y)^n form?

<p>Pascal's triangle (A)</p> Signup and view all the answers

In combinatorics, what does (n choose b) represent?

<p>The number of combinations of b elements from an n-element set (D)</p> Signup and view all the answers

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Study Notes

Binomial Theorem

  • The polynomial (x + y)^n can be expanded according to the binomial theorem, which describes the algebraic expansion of powers of a binomial.
  • The binomial theorem is a fundamental concept in elementary algebra that describes the expansion of powers of a binomial into a sum of terms involving various powers of the individual terms.

Exponents b and c

  • In the expansion of (x + y)^n, the exponents b and c are required to satisfy the condition b + c = n, where b and c are non-negative integers.

Coefficients in the Expansion

  • The coefficients in the expansion of (x + y)^n form a symmetric sequence, with the first and last coefficients being 1 and the coefficients in between being binomial coefficients.

Combinatorics

  • In combinatorics, (n choose b) represents the number of ways to choose b items from a set of n items, also known as the binomial coefficient.
  • (n choose b) is calculated as n!/b!(n-b)!, where ! denotes the factorial function.

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