The Binomial Theorem Answers

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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)
2
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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.
3

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
4

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
5

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

A
0
B
1
C
9
D
10
6

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
7

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

A
8
B
9
C
10
D
11
8

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.
9

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
10

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

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