
Binomial Expansion

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is Binomial Expansion?
Back
Binomial Expansion is a method used to expand expressions that are raised to a power, specifically in the form (a + b)^n, where 'a' and 'b' are any numbers, and 'n' is a non-negative integer.
2.
FLASHCARD QUESTION
Front
What is the Binomial Theorem?
Back
The Binomial Theorem provides a formula for the expansion of (a + b)^n, expressed as: (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n.
3.
FLASHCARD QUESTION
Front
What does (n choose k) represent?
Back
(n choose k), denoted as C(n, k) or nCk, represents the number of ways to choose k elements from a set of n elements without regard to the order of selection.
4.
FLASHCARD QUESTION
Front
How do you find the constant term in a binomial expansion?
Back
To find the constant term in the expansion of (a + b)^n, set the variable part to zero and solve for the corresponding term.
5.
FLASHCARD QUESTION
Front
What is the formula for the k-th term in the expansion of (a + b)^n?
Back
The k-th term in the expansion of (a + b)^n is given by T(k) = C(n, k-1) * a^(n-(k-1)) * b^(k-1).
6.
FLASHCARD QUESTION
Front
How do you determine the coefficient of a specific term in a binomial expansion?
Back
To determine the coefficient of a specific term a^m * b^n in the expansion of (a + b)^n, use the formula C(n, n-m) * a^m * b^n.
7.
FLASHCARD QUESTION
Front
What is the fourth term in the expansion of (x + y)^5?
Back
The fourth term is given by T(4) = C(5, 3) * x^(5-3) * y^3 = 10xy^3.
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