Mastering the Binomial Theorem

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

• x^4 + 8x^3 + 24x^2 + 32x + 16

• x^4 + 6x^3 + 12x^2 + 16x + 12

• x^4 + 10x^3 + 20x^2 + 30x + 20

• x^4 + 4x^3 + 6x^2 + 8x + 8

Use the binomial theorem to expand (a + b)^3.

• a^3 + 3ab + b^3

• a^3 + 3a^2b + b^3

• a^3 + 3a^2b + 3ab^2 + b^3

• a^3 + 2a^2b + 2ab^2 + b^3

Identify the coefficient of x^3 in the expansion of (2x + 3)^6.

• 2160

• 720

• 4320

• 8640

What is the coefficient of x^2 in the expansion of (3x - 5)^5?

• 2250

• 3000

• 1500

• 1800

Expand (x - 1)^5 using the binomial theorem.

• x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1

• x^5 - 4x^4 + 6x^3 - 4x^2 + 2x - 1

• x^5 - 5x^4 + 10x^3 - 10x^2 + 10x + 1

• x^5 - 5x^4 + 10x^3 - 5x^2 + 5 - 1

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

• 54

• 108

• 162

• 216

Apply the binomial theorem to find the expansion of (x + 1)^2.

• 2x + 1

• x^2 + 1

• x^2 + 2x + 1

• x^2 + 2

Using Pascal's triangle, what is the coefficient of x^4 in (x + 2)^6?

• 75

• 30

• 45

• 60

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

• 2x^3 - 9x^2y + 12xy^2 - 3y^3

• 6x^3 - 27x^2y + 36xy^2 - 18y^3

• 8x^3 - 36x^2y + 54xy^2 - 27y^3

• 4x^3 - 12x^2y + 18xy^2 - 8y^3

Identify the coefficient of x^5 in the expansion of (x + 4)^7.

• 420

• 256

• 128

• 336