Binomial Theorem

Front

What is the Binomial Theorem?

Back

The Binomial Theorem provides a formula for the expansion of powers of a binomial (a + b)^n, expressed as the sum of terms involving coefficients from Pascal's Triangle.

Front

What is the formula for the nth term in the expansion of (a + b)^n?

Back

The nth term is given by T(n+1) = C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient.

Front

What is a binomial coefficient?

Back

A binomial coefficient, 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.

Front

How do you calculate the binomial coefficient C(n, k)?

Back

C(n, k) = n! / (k! * (n-k)!), where n! is the factorial of n.

Front

What is the expansion of (x + y)^2?

Back

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

Front

What is the expansion of (x + y)^3?

Back

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

Front

What is the 5th term of the expansion of (n + 4)^4?

Back

256.

Front

What is the 4th term of the expansion of (a + 3)^4?

Back

108a.

Front

What are the coefficients of the 5th row in Pascal's Triangle?

Back

1; 4; 6; 4; 1.

Front

What is the expansion of (x + 1)^5?

Back

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