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Mastering Binomial Expansion

Authored by John Njau

Mathematics

12th Grade

Used 13+ times

Mastering Binomial Expansion
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15 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the binomial theorem?

The binomial theorem states that (a - b)^n = Σ (n choose k) * a^(n+k) * b^k.

The binomial theorem is used to calculate the area of a circle.

The binomial theorem states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k.

The binomial theorem is a method for solving quadratic equations.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Expand (a + b)^3 using the binomial theorem.

a^3 + 3a^2b + 3ab^2 + b^3

a^3 + 2a^2b + 2ab^2 + b^3

a^3 + 3a^2b + b^3

a^3 + 3ab + b^3

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the coefficient of x^2 in the expansion of (2x + 3)^4?

81

216

108

64

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many terms are in the expansion of (x + y)^5?

8

6

7

5

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Expand (x - 2)^4 using the binomial theorem.

x^4 - 4x^3 + 6x^2 - 8x + 4

x^4 - 8x^3 + 24x^2 - 32x + 16

x^4 - 6x^3 + 12x^2 - 16x + 8

x^4 - 10x^3 + 30x^2 - 40x + 20

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the general term in the expansion of (a + b)^n?

T_k = (n + k) * a^k * b^(n-k)

T_k = (n choose k) * a^(n-k) * b^k

T_k = a^n + b^n

T_k = n! / (k! * (n-k)!) * a^k * b^k

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Calculate the value of the 5th term in the expansion of (3x + 2)^6.

1800x^2

1296x^2

2160x^2

864x^2

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