Mastering Binomial Expansion

What is the binomial coefficient for the term x^3 in the expansion of (x + 2)^5?

• 40

• 20

• 50

• 30

Expand the expression (3x - 4)^4 using the binomial theorem.

• 27x^4 - 48x^3 + 36x^2 - 16x + 64

• 81x^4 + 108x^3 + 144x^2 + 64x + 256

• 81x^4 - 54x^3 + 36x^2 - 16x + 256

• 81x^4 - 108x^3 + 144x^2 - 64x + 256

Identify the binomial coefficient for the term y^2 in the expansion of (2y + 5)^6.

• 25000

• 45000

• 30000

• 37500

Using the binomial expansion, what is the coefficient of x^2 in (x + 1)^6?

• 15

• 10

• 20

• 5

Expand (a + b)^3 and list all the terms with their coefficients.

• a^3 + 3a^2b + 2ab^2 + 2b^3

• a^3 + 3a^2b + 3ab^2 + b^3

• a^3 + 2a^2b + 4ab^2 + b^3

• a^3 + 3a^2b + 3ab^2 + 2b^3

What is the value of the binomial coefficient C(5, 2)?

• 5

• 15

• 10

• 20

Expand (2x - 3y)^2 and simplify the expression.

• 4x^2 - 12xy + 9y^2

• 8x^2 - 9y^2

• 2x^2 - 6xy + 3y^2

• 4x^2 + 6xy + 9y^2

In the expansion of (x + 1)^7, what is the coefficient of x^5?

• 21

• 35

• 28

• 14

What is the value of the binomial coefficient C(6, 3)?

• 20

• 15

• 30

• 10

Using the binomial expansion, what is the coefficient of x^3 in (2x + 1)^5?

• 10

• 20

• 30

• 40