The Binomial Theorem Quiz

How many terms are in the binomial expansion of (2x + 3)5? 4 5 6 7

c: 6

What is the binomial expansion of (2x - 3)5? (2x)5 - 15(2x)4 + 90(2x)3 - 270(2x)2 + 405(2x) - 243 (2x)5 + 15(2x)4 - 90(2x)3 + 270(2x)2 - 405(2x) + 243 (2x)5 + 15(2x)4 + 90(2x)3 + 270(2x)2 + 405(2x) + 243 2(x)5 - 30(x)4 + 180(x)3 - 540(2x)2 + 810(x) - 243

a: (2x)5 - 15(2x)4 + 90(2x)3 - 270(2x)2 + 405(2x) - 243

Which expression represents the fourth term in the binomial expansion of (e + 2f)10? 10C3(e7)(2f)3 10C3(e7)(f)3 10C4(e6)(2f)4 10C4(e6)(f)4

a: 10C3(e7)(2f)3

The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube? 64x6 + 144x4 + 108x2 + 27 64x6 + 48x4 + 12x2 + 1 4x6 + 36x4 + 108x2 + 27 4x6 + 12x4 +12x2 + 1

a: 64x6 + 144x4 + 108x2 + 27

What are the coefficients for the binomial expansion of (p + q)6? 1, 8, 28, 56, 70, 56, 28, 8, 1 1, 6, 15, 20, 15, 6, 1 1, 5, 10, 10, 5, 1 1, 4, 6, 4, 1

b: 1, 6, 15, 20, 15, 6, 1

What is the coefficient of the third term in the binomial expansion of (a + b)6? 1 15 20 90

b: 15

How many terms are in the binomial expansion of (3x + 5)9? 8 9 10 11

c: 10

Which statement about the simplified binomial expansion of (a + b)n, where n is a positive integer, is true? The value of the binomial coefficient nC0 is n - 1 for all values of n. The values of nC1 and nCn-1 are equal to 1. The values of nC0 and nCn are equal to 1. The value of the binomial coefficient nC1 is n - 1 for all values of n.

c: The values of nC0 and nCn are equal to 1.

What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2 + 8x + 2

c: x4 + 8x3 + 24x2 + 32x + 16

What is the coefficient of the x4-term in the binomial expansion of (x + 3)12? 12C7(3)7 12C8 12C4(3)4 12C8(3)8

d: 12C8(3)8