The Binomial Theorem

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 is Pascal's Triangle?

Back

Pascal's Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it. It is used to find coefficients in the expansion of (a + b)^n.

Front

What is a Monomial?

Back

A monomial is a polynomial with only one term, such as 3x^2 or -5.

Front

What is a Binomial?

Back

A binomial is a polynomial with two terms, such as (x + 2) or (3x^2 - 1).

Front

What is a Trinomial?

Back

A trinomial is a polynomial with three terms, such as (x^2 + 3x + 2).

Front

What is a Polynomial?

Back

A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Front

How do you expand (a + b)^n using the Binomial Theorem?

Back

To expand (a + b)^n, use the formula: (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Front

What is the formula for (n choose k)?

Back

The formula for (n choose k) is n! / (k!(n-k)!), where n! is the factorial of n.

Front

What is the 7th row of Pascal's Triangle?

Back

The 7th row of Pascal's Triangle is 1, 7, 21, 35, 35, 21, 7, 1.

Front

Expand (2x + 5)^4 using the Binomial Theorem.

Back

(2x + 5)^4 = 16x^4 + 160x^3 + 600x^2 + 1000x + 625.