Binomial Expansion

Front

What is Binomial Expansion?

Back

Binomial Expansion is the process of expanding expressions that are raised to a power, specifically in the form (a + b)^n, using the Binomial Theorem.

Front

State the Binomial Theorem.

Back

The Binomial Theorem states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k = 0 to n.

Front

What does (n choose k) represent in the Binomial Theorem?

Back

(n choose k) represents the number of ways to choose k elements from a set of n elements, calculated as n! / (k!(n-k)!).

Front

Expand (x + y)^2.

Back

(x + y)^2 = x^2 + 2xy + y^2.

Front

Expand (x + y)^3.

Back

(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3.

Front

What is the fourth term in the expansion of (a + b)^5?

Back

The fourth term is 5 * a^2 * b^3.

Front

How do you find the coefficients in a binomial expansion?

Back

Coefficients can be found using Pascal's Triangle or by calculating (n choose k) for each term.

Front

What is Pascal's Triangle?

Back

Pascal's Triangle is a triangular array of numbers where each number is the sum of the two directly above it, used to find coefficients in binomial expansions.

Front

Expand (1 - x)^5.

Back

(1 - x)^5 = 1 - 5x + 10x^2 - 10x^3 + 5x^4 - x^5.

Front

What is the third term in the expansion of (x + 4)^5?

Back

The third term is 160x^3.