Binomial Expansion (Pascal)

Front

What is Binomial Expansion?

Back

Binomial Expansion is a method used to expand expressions that are raised to a power, typically in the form (a + b)^n, using coefficients from Pascal's Triangle.

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 coefficients in binomial expansions.

Front

What is the formula for the Binomial Theorem?

Back

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

Front

How do you find the coefficients in a binomial expansion?

Back

Coefficients can be found using the binomial coefficients, which are the entries in Pascal's Triangle corresponding to the row number n.

Front

What is the 3rd row of Pascal's Triangle?

Back

The 3rd row of Pascal's Triangle is 1, 3, 3, 1.

Front

Expand (x + y)^2.

Back

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

Front

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

Back

The 4th term is 10x^2y^3.

Front

Expand (x - 2y)^3.

Back

(x - 2y)^3 = x^3 - 6x^2y + 12xy^2 - 8y^3.

Front

What is the significance of the row number in Pascal's Triangle?

Back

The row number corresponds to the exponent in the binomial expansion (a + b)^n.

Front

What is the 5th row of Pascal's Triangle?

Back

The 5th row of Pascal's Triangle is 1, 5, 10, 10, 5, 1.