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 does (y - 3)(y + 7) equal?

Back

y^2 + 4y - 21

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, and it is used to find coefficients in binomial expansions.

Front

How do you find the sum of two polynomials?

Back

To find the sum of two polynomials, combine like terms by adding their coefficients.

Front

What is the formula for combinations?

Back

The formula for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Front

How many combinations of 3 bracelets can Kamali choose from 7?

Back

35

Front

What does (3 - 2x + 2x^2) - (4x - 5 + 3x^2) equal?

Back

-x^2 - 6x + 8

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as (a + b) or (x - 5).

Front

What is the significance of the coefficients in the Binomial Theorem?

Back

The coefficients in the Binomial Theorem correspond to the values in Pascal's Triangle and represent the number of ways to choose k elements from n.