Pascal's Triangle and Binomial Theorem

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.

Tags

CCSS.HSA.APR.C.5

Front

What is the Binomial Theorem?

Back

The Binomial Theorem describes the algebraic expansion of powers of a binomial. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Tags

CCSS.HSA.APR.C.5

Front

What does (n choose k) represent?

Back

(n choose k) or C(n, k) represents the number of ways to choose k elements from a set of n elements without regard to the order of selection.

Front

How do you find the third term in the expansion of (a + b)^n?

Back

The third term is given by the formula T(k+1) = (n choose k) * a^(n-k) * b^k, where k = 2 for the third term.

Tags

CCSS.HSA.APR.C.5

Front

What is the formula for the k-th term in the expansion of (a + b)^n?

Back

T(k+1) = (n choose k) * a^(n-k) * b^k.

Tags

CCSS.HSA.APR.C.5

Front

What is the expansion of (x + 1)^5?

Back

x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.

Tags

CCSS.HSA.APR.C.5

Front

How do you determine the coefficients in the expansion of (a + b)^n?

Back

The coefficients are found in the n-th row of Pascal's Triangle.

Tags

CCSS.HSA.APR.C.5

Front

What is the fourth term in the expansion of (4x - 3)^5?

Back

-4320x^2.

Tags

CCSS.HSA.APR.C.5

Front

How do you find the 14th term in the expansion of (2x - y)^18?

Back

Use the formula T(k+1) = (n choose k) * (2x)^(n-k) * (-y)^k, where k = 13 for the 14th term.

Tags

CCSS.HSA.APR.C.5

Front

What is the significance of the row in Pascal's Triangle for (x + y)^3?

Back

The coefficients for the expansion of (x + y)^3 are found in the row 1 3 3 1 of Pascal's Triangle.

Tags

CCSS.HSA.APR.C.5