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?

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.

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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

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

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

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

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

–73,728r11s

73,728r11s

608,256r10s2

–608,256r10s2

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

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

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

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

The first term is –x18.

The second term is 9x17.

The third term is 36x14.

The last term is –x9.

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