Binomial theorem

Pascal's Triangle

Multiple Choice

The term independent of x in the expansion of $$\ \left(x^3+\frac{3}{x^2}\right)^{15}\$$  is

• $$\ ^{15}C_9\left(3\right)^9$$  

• $$\ ^{15}C_6\left(3\right)^6$$  

• $$\ ^{15}C_9\left(3\right)^4$$  

• $$\ ^{15}C_9\left(3\right)^7$$  

Fill in the Blanks

If (a + 5x)(1 + 4x)ⁿ = 11 + 313x + bx² + ..., where a and b are constants and n is a positive integer. The value of n is

.

Fill in the Blanks

In the expansion of (1 - 3x)ⁿ + (1 + x)ⁿ, where n is a positive integer, the coefficient of x² is 150. The value of n is

.

Multiple Choice

Find the constant term in $$\left(x+\frac{1}{x}\right)^{10}$$  

• $$252$$

• $$210$$

• $$45$$

• $$120$$

Multiple Choice

Multiple Choice

How many terms are the in the expansion of (1+b)⁵

• 5

• 6

• 25

• 50

• 3

Multiple Choice

What is the Binomial expansion of (x + 1)⁵ ?

• x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

• x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

• x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

• x⁵ + 1

Multiple Choice

Select the correct expansion of

(1 - x)⁵

• 1 − 5x + 10x² − 10x³ + 5x⁴ − x⁵

• 1 + 5x + 10x² + 10x³ + 5x⁴ + x⁵

• -1 + 5x - 10x² + 10x³ - 5x⁴ + x⁵

• 1 − 5x + 10x² + 10x³ + 5x⁴ − x⁵

Multiple Choice

Select the correct expansion of

(1 + 4x)³

• 1 + 12x + 12x² + 4x³

• 1 + 12x + 48x² + 64x³

• 1 + 3x + 3x² + x³

• 1 + 4x + 16x² + 64x³

Multiple Choice

Find the value of...

₈C₅

• 56

• 70

• 8

• 28

Multiple Choice

Find the coefficient of x³ in the expansion of (1 + x)²⁰

• 1140

• 190

• 4845

• 8000

Multiple Choice

Find the coefficient of x⁴ in the expansion of (1 - x)¹⁴

• 1001

• -1001

• 364

• -364

Combination refers to a list of numbers where the order doesn't matter at all.

Multiple Choice

Find the term containing $$x^5$$  in the expansion of  $$\left(2y+x\right)^7$$  

• $$84y^2x^5$$  

• $$280y^3x^5$$  

• $$672y^2x^5$$  

• $$14y^3x^5$$