Binomial Theorem Flashcard

Front

What is the Binomial Theorem?

Back

The Binomial Theorem provides a formula for the expansion of powers of a binomial, expressed as: (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k = 0 to n.

Tags

CCSS.HSA.APR.C.5

Front

What does 'n choose k' mean in the context of the Binomial Theorem?

Back

'n choose k', denoted as C(n, k) or nCk, represents the number of ways to choose k elements from a set of n elements without regard to the order of selection. It is calculated as: C(n, k) = n! / (k!(n-k)!).

Tags

CCSS.HSA.APR.C.5

Front

How do you find the coefficient of a specific term in a binomial expansion?

Back

To find the coefficient of a term a^k * b^(n-k) in the expansion of (a + b)^n, use the formula: Coefficient = C(n, k) * a^k * b^(n-k).

Tags

CCSS.HSA.APR.C.5

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 provides a quick way to find coefficients for binomial expansions.

Tags

CCSS.HSA.APR.C.5

Front

How many rows are in Pascal's Triangle?

Back

Pascal's Triangle has an infinite number of rows.

Tags

CCSS.HSA.APR.C.5

Front

What is the 6th term of the expansion of (m - 3)^5?

Back

The 6th term is -243.

Tags

CCSS.HSA.APR.C.5

Front

Find the 4th term in the expansion of (4x - 3)^5.

Back

The 4th term is -4320x^2.

Tags

CCSS.HSA.APR.C.5

Front

What is the third term for the expansion (2x - 5)^5?

Back

The third term is 2000x^3.

Tags

CCSS.HSA.APR.C.5

Front

Calculate the coefficient of a^4b^6 in the expansion of (a + b)^{10}.

Back

The coefficient is 210.

Tags

CCSS.HSA.APR.C.5

Front

What is the general form of a term in the expansion of (a + b)^n?

Back

The general term T(k+1) in the expansion of (a + b)^n is given by T(k+1) = C(n, k) * a^(n-k) * b^k.

Tags

CCSS.HSA.APR.C.5