Exploring the Binomial Theorem

What is the Binomial Theorem?

• The Binomial Theorem is used to solve linear equations.

• The Binomial Theorem states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k.

• The Binomial Theorem applies only to quadratic equations.

• The Binomial Theorem states that (a - b)^n = Σ (n choose k) * a^(n+k) * b^k.

Tags

CCSS.HSA.APR.C.5

State the general form of the Binomial Theorem.

• (a + b)^n = C(n, k) * a^k * b^(n-k) for k = 1 to n.

• (a + b)^n = Σ (C(n, k) * a^k * b^(n-k)) for k = 0 to n.

• (a + b)^n = (a^n + b^n) for n > 0.

• (a + b)^n = Σ (C(n, k) * a^(n-k) * b^k) for k = 0 to n.

Tags

CCSS.HSA.APR.C.5

What is the value of (a + b)^2 using the Binomial Theorem?

• a^2 + b^2

• 2a + 2b

• a^2 + 2b^2

• a^2 + 2ab + b^2

Tags

CCSS.HSA.APR.C.5

Calculate the coefficient of x^3 in the expansion of (2x + 3)^5.

• 720

• 540

• 600

• 800

Tags

CCSS.HSA.APR.C.5

What is the significance of Pascal's Triangle in relation to the Binomial Theorem?

• Pascal's Triangle is a method for solving linear equations.

• Pascal's Triangle is significant as it provides the coefficients for the expansion of the Binomial Theorem.

• Pascal's Triangle is used to calculate prime numbers.

• Pascal's Triangle represents the Fibonacci sequence.

Tags

CCSS.HSA.APR.C.5

Expand (x - 2)^4 using the Binomial Theorem.

• x^4 - 4x^3 + 6x^2 - 8x + 4

• x^4 - 10x^3 + 30x^2 - 40x + 20

• x^4 - 6x^3 + 12x^2 - 16x + 8

• x^4 - 8x^3 + 24x^2 - 32x + 16

Tags

CCSS.HSA.APR.C.5

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

• n

• 2n

• n - 1

• n + 1

Tags

CCSS.HSA.APR.C.5

What is the formula for the binomial coefficient?

• C(n, k) = n! / (k! * (n - k)!)

• C(n, k) = (n + k)! / (n! * k!)

• C(n, k) = n! / (k! * n!)

• C(n, k) = n! / (k! * (n + k)!)

If n = 6, what is the coefficient of a^2b^4 in the expansion of (a + b)^6?

• 15

• 10

• 20

• 5

Tags

CCSS.HSA.APR.C.5

Explain how the Binomial Theorem can be used to approximate powers of binomials.

• The Binomial Theorem only applies to single variables.

• The Binomial Theorem can be used to approximate powers of binomials by expanding (a + b)^n into a series and simplifying the expression.

• The Binomial Theorem is only valid for positive integers.

• The Binomial Theorem cannot be used for approximations.

Tags

CCSS.HSA.APR.C.5