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 is the formula for finding the coefficients in Pascal's Triangle?

Back

The coefficients in Pascal's Triangle can be found using the formula C(n, k) = n! / (k!(n-k)!), where n is the row number and k is the position in that row.

Tags

CCSS.HSA.APR.C.5

Front

How many terms are in the expansion of (a + b)^n?

Back

The number of terms in the expansion of (a + b)^n is n + 1.

Tags

CCSS.HSA.APR.C.5

Front

What is the 5th row of Pascal's Triangle?

Back

The 5th row of Pascal's Triangle is 1; 5; 10; 10; 5; 1.

Tags

CCSS.HSA.APR.C.5

Front

How do you find the element in Pascal's Triangle at row n and position k?

Back

The element at row n and position k can be found using the binomial coefficient C(n, k).

Tags

CCSS.HSA.APR.C.5

Front

What is the value of C(12, 5)?

Back

C(12, 5) = 792.

Front

What is the value of C(8, 6)?

Back

C(8, 6) = 28.

Front

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

Back

The expansion of (x + 1)^5 is x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.

Tags

CCSS.HSA.APR.C.5

Front

What is the significance of the coefficients in the binomial expansion?

Back

The coefficients in the binomial expansion represent the number of ways to choose k elements from a set of n elements.

Tags

CCSS.HSA.APR.C.5