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 in the form of 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 'n choose k', represents the number of ways to choose k elements from a set of n elements without regard to the order of selection.

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. It is used to find binomial coefficients.

Front

How do you find the 7th row of Pascal's Triangle?

Back

The 7th row of Pascal's Triangle corresponds to the coefficients of the expansion of (a + b)^7, which are 1, 7, 21, 35, 35, 21, 7, 1.

Front

What is the formula for the nth term of a binomial expansion?

Back

The nth term of the expansion of (a + b)^n is given by T(k+1) = C(n, k) * a^(n-k) * b^k, where k is the term number starting from 0.

Front

What is the 2nd term of the expansion of (y + 4)^4?

Back

The 2nd term is 256y.

Front

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

Back

The 5th term is 256.

Front

Expand (x - 7)^2.

Back

The expansion is x^2 - 14x + 49.

Front

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

Back

The 4th term is 108a.

Front

What is the general term in the expansion of (x + y)^n?

Back

The general term is T(k+1) = C(n, k) * x^(n-k) * y^k.