Binomial Expansion

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 (x + 1)^5 expand to using the Binomial Theorem?

Back

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

Tags

CCSS.HSA.APR.C.5

Front

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

Back

Use the formula for the binomial coefficient, which is (n choose k) = n! / (k!(n-k)!), where n is the exponent and k is the term number.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

The nth 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 significance of the coefficients in a binomial expansion?

Back

The coefficients represent the number of ways to choose k elements from n, which corresponds to the number of combinations.

Tags

CCSS.HSA.APR.C.5

Front

What is the expansion of (x + y)^3?

Back

x^3 + 3x^2y + 3xy^2 + y^3.

Tags

CCSS.HSA.APR.C.5

Front

How do you determine the fourth term in the expansion of (5 + 3y)^5?

Back

Use the formula T(k+1) = (n choose k) * a^(n-k) * b^k, where n=5, a=5, b=3y, and k=3.

Tags

CCSS.HSA.APR.C.5

Front

What is the third term in the expansion of (x + 4)^5?

Back

The third term is 160x^3.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

The fourth term is -4320x^2.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

They determine the weight of each term in the expansion based on the number of ways to select terms.

Tags

CCSS.HSA.APR.C.5