BINOMIAL EXPANSION AND PASCALS TRIANGLE

Front

What is the Binomial Theorem?

Back

The Binomial Theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Front

What does Pascal's Triangle represent?

Back

Pascal's Triangle is a triangular array of numbers where each number is the sum of the two directly above it. It represents the coefficients in the binomial expansion and can be used to find combinations.

Front

How do you find the number of terms in the expansion of (a + b)^n?

Back

The number of terms in the expansion of (a + b)^n is given by n + 1.

Front

What is the formula for the binomial coefficient?

Back

The binomial coefficient, denoted as (n choose k), is calculated as (n!)/(k!(n-k)!), where n! is the factorial of n.

Front

What is the fifth term in the expansion of (3x - 4)^4?

Back

The fifth term is 256.

Front

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

Back

The expansion is x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.

Front

Which row of Pascal's Triangle corresponds to (x + y)^3?

Back

The row is 1, 3, 3, 1.

Front

What is the significance of the coefficients in Pascal's Triangle?

Back

The coefficients in Pascal's Triangle represent the number of ways to choose k elements from a set of n elements, which corresponds to the binomial coefficients in the expansion.

Front

How do you calculate the nth row of Pascal's Triangle?

Back

To calculate the nth row, start with 1, and each subsequent number is the sum of the two numbers directly above it.

Front

What is the relationship between binomial expansion and combinatorics?

Back

Binomial expansion uses combinatorial principles to determine the coefficients of the expanded terms, representing the number of ways to choose elements.