The Binomial Theorem Answers

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Which statement about the simplified binomial expansion of (a + b)n, where n is a positive integer, is true?

A
The value of the binomial coefficient nC0 is n – 1 for all values of n.
B
The values of nC1 and nCn–1 are equal to 1.
C
The values of nC0 and nCn are equal to 1.
D
The value of the binomial coefficient nC1 is n – 1 for all values of n.
2
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Which expression represents the fourth term in the binomial expansion of (e + 2f)10?

A
10C3(e7)(2f)3
B
10C3(e7)(f)3
C
10C4(e6)(2f)4
D
10C4(e6)(f)4
3

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

A
4
B
5
C
6
D
7
4

What is the coefficient of the last term in the binomial expansion of (x + 1)9?

A
0
B
1
C
9
D
10
5

What is the binomial expansion of (2x – 3)5?

A
(2x)5 – 15(2x)4 + 90(2x)3 – 270(2x)2 + 405(2x) – 243
B
(2x)5 + 15(2x)4 – 90(2x)3 + 270(2x)2 – 405(2x) + 243
C
(2x)5 + 15(2x)4 + 90(2x)3 + 270(2x)2 + 405(2x) + 243
D
2(x)5 – 30(x)4 + 180(x)3 – 540(2x)2 + 810(x) – 243
6

What is the second term in the binomial expansion of (2r – 3s)12?

A
–73,728r11s
B
73,728r11s
C
608,256r10s2
D
–608,256r10s2
7

What is the coefficient of the x4-term in the binomial expansion of (x + 3)12?

A
12C7(3)7
B
12C8
C
12C4(3)4
D
12C8(3)8
8

What are the coefficients for the binomial expansion of (p + q)6?

A
1, 8, 28, 56, 70, 56, 28, 8, 1
B
1, 6, 15, 20, 15, 6, 1
C
1, 5, 10, 10, 5, 1
D
1, 4, 6, 4, 1
9

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

A
8
B
9
C
10
D
11
10

Which statement about the binomial expansion of (x2 – x)9 is true?

A
The first term is –x18.
B
The second term is 9x17.
C
The third term is 36x14.
D
The last term is –x9.
11

What is the coefficient of the x5y5-term in the binomial expansion of (2x – 3y)10?

A
10C5(2)5(3)5
B
10C5(2)5(–3)5
C
–10C5(2)5(–3)5
D
10C5(2)5(3)
12

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

A
1
B
15
C
20
D
90
13

What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4?

A
4
B
32
C
128
D
512
14

The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube?

A
64x6 + 144x4 + 108x2 + 27
B
64x6 + 48x4 + 12x2 + 1
C
4x6 + 36x4 + 108x2 + 27
D
4x6 + 12x4 +12x2 + 1
15

The following list gives the coefficients for the binomial expansion of (x + y)10. What is the value of B? 1, 10, 45, 120, 210, 252, 210, B, 45, 10, 1

A
1
B
10
C
45
D
120
16

What is the binomial expansion of (x + 2)4?

A
x4 + 4x3 + 6x2 + 4x + 1
B
8x3 + 24x2 + 32x
C
x4 + 8x3 + 24x2 + 32x + 16
D
2x4 + 8x3 + 12x2 + 8x + 2

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