Binomial Expansion

Binomial Expansion

Assessment

Flashcard

Mathematics

11th - 12th Grade

Hard

Created by

Wayground Content

FREE Resource

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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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