Binomial Theorem

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 ranges from 0 to n.

Tags

CCSS.HSA.APR.C.5

Front

What does (m - 3)^5 represent in the context of the Binomial Theorem?

Back

It represents a binomial expression raised to the 5th power, which can be expanded using the Binomial Theorem.

Tags

CCSS.HSA.APR.C.5

Front

How do you find the 6th term of the expansion of (m - 3)^5?

Back

Use the formula for the k-th term: T(k+1) = (n choose k) * a^(n-k) * b^k. For (m - 3)^5, the 6th term is T(6) = (5 choose 5) * m^(5-5) * (-3)^5 = -243.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

The k-th term is given by T(k+1) = (n choose k) * a^(n-k) * b^k.

Tags

CCSS.HSA.APR.C.5

Front

What is the value of (n choose k)?

Back

It is calculated as n! / (k! * (n-k)!), representing the number of ways to choose k elements from a set of n elements.

Tags

CCSS.HSA.APR.C.5

Front

Expand (d - 5)^5 using the Binomial Theorem.

Back

d^5 - 25d^4 + 250d^3 - 1250d^2 + 3125d - 3125.

Tags

CCSS.HSA.APR.C.5

Front

What is the Binomial 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 2nd term of the expansion of (y + 4)^4?

Back

Use T(2) = (4 choose 1) * y^(4-1) * 4^1 = 16y^3.

Tags

CCSS.HSA.APR.C.5

Front

What is the 5th term of the expansion of (n + 4)^4?

Back

The 5th term is T(5) = (4 choose 4) * n^(4-4) * 4^4 = 256.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

The coefficients correspond to the binomial coefficients (n choose k) and represent the number of ways to choose k elements from n.

Tags

CCSS.HSA.APR.C.5