AlGeo 3 The Binomial Theorem

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)

B) 10C5(2)5(-3)5

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

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

C)10

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

B) 15

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 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

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
1
10
45
120

Not, B) 10

What is the binomial expansion of (x + 2)4?
x4 + 4×3 + 6×2 + 4x + 1
8×3 + 24×2 + 32x
x4 + 8×3 + 24×2 + 32x + 16
2×4 + 8×3 + 12×2 + 8x + 2

C) x4 + 8×3 + 24×2 + 32x + 16

What is the coefficient of the last term in the binomial expansion of (x + 1)9?
0
1
9
10

B) 1

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

Not, A) 4

The side length, s, of a cube is 4×2 + 3. If V = s3, what is the volume of the cube?
64×6 + 144×4 + 108×2 + 27
64×6 + 48×4 + 12×2 + 1
4×6 + 36×4 + 108×2 + 27
4×6 + 12×4 +12×2 + 1

A) 64×6 + 144×4 + 108×2 + 27

What is the coefficient of the x9y-term in the binomial expansion of (2y + 4×3)4?
4
32
128
512

D) 512

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

Not, B) (2x)5 + 15(2x)4 – 90(2x)3 + 270(2x)2 – 405(2x) + 243