Mastering Binomial Expansion

What is the binomial theorem?

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

• The binomial theorem is used to calculate the area of a circle.

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

• The binomial theorem is a method for solving quadratic equations.

Expand (a + b)^3 using the binomial theorem.

• a^3 + 3a^2b + 3ab^2 + b^3

• a^3 + 2a^2b + 2ab^2 + b^3

• a^3 + 3a^2b + b^3

• a^3 + 3ab + b^3

What is the coefficient of x^2 in the expansion of (2x + 3)^4?

• 81

• 216

• 108

• 64

How many terms are in the expansion of (x + y)^5?

• 8

• 6

• 7

• 5

Expand (x - 2)^4 using the binomial theorem.

• x^4 - 4x^3 + 6x^2 - 8x + 4

• x^4 - 8x^3 + 24x^2 - 32x + 16

• x^4 - 6x^3 + 12x^2 - 16x + 8

• x^4 - 10x^3 + 30x^2 - 40x + 20

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

• T_k = (n + k) * a^k * b^(n-k)

• T_k = (n choose k) * a^(n-k) * b^k

• T_k = a^n + b^n

• T_k = n! / (k! * (n-k)!) * a^k * b^k

Calculate the value of the 5th term in the expansion of (3x + 2)^6.

• 1800x^2

• 1296x^2

• 2160x^2

• 864x^2

If (x + y)^n has 10 terms, what is the value of n?

• 11

• 8

• 9

• 5

Expand (2x - 3y)^3 using the binomial theorem.

• 8x^3 - 36x^2y + 27xy^2 - 27y^3

• 8x^3 - 27x^2y + 36xy^2 - 27y^3

• 4x^3 - 12x^2y + 9xy^2 - 9y^3

• 2x^3 - 18x^2y + 27xy^2 - 18y^3

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

• 32

• 20

• 25

• 30