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 specific term in the expansion of (a + b)^n, use the formula: Coefficient = C(n, k) * a^(n-k) * b^k, where k is the exponent of b in the term.

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 in the expansion of (3x + 2)^8?

Back

The 6th term is 48384x^3.

Tags

CCSS.HSA.APR.C.5

Front

How do you find the coefficient of the x^5 term in (5x + 1)^{11}?

Back

The coefficient of the x^5 term is found using the formula: C(11, 5) * (5x)^5 * (1)^(11-5) = 1443750.

Tags

CCSS.HSA.APR.C.5

Front

What is the fourth term in the expansion of (\frac{x}{2} + y)^7?

Back

The fourth term is \frac{35x^4y^3}{16}.

Tags

CCSS.HSA.APR.C.5

Front

What are the coefficients of the 5th row in Pascal's Triangle?

Back

The coefficients of the 5th row are 1; 5; 10; 10; 5; 1.

Tags

CCSS.HSA.APR.C.5

Front

What is the general form of a term in the binomial 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