What is the Binomial Theorem?
Binomial Expansion

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Mathematics
•
8th - 11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
The Binomial Theorem provides a formula for the expansion of powers of a binomial, expressed as (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n.
2.
FLASHCARD QUESTION
Front
What does (n choose k) represent in the Binomial Theorem?
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.
3.
FLASHCARD QUESTION
Front
How do you find 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), where k starts from 1.
4.
FLASHCARD QUESTION
Front
What is the fourth term in the expansion of (5 + 3y)^5?
Back
The fourth term is 6750y^3.
5.
FLASHCARD QUESTION
Front
What is the expansion of (1 + 4x)^3?
Back
The expansion is 1 + 12x + 48x^2 + 64x^3.
6.
FLASHCARD QUESTION
Front
What is the expansion of (1 - x)^5?
Back
The expansion is 1 - 5x + 10x^2 - 10x^3 + 5x^4 - x^5.
7.
FLASHCARD QUESTION
Front
What is the Binomial expansion of (x + 1)^5?
Back
The expansion is x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.
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