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.

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

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

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

10C5(2)5(3)5

10C5(2)5(–3)5

–10C5(2)5(–3)5

10C5(2)5(3)

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

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

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

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