Binomial theorem

Presentation

•

Mathematics

•

10th Grade

•

Hard

John BIDDULPH

Used 1+ times

FREE Resource

2 Slides • 13 Questions

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

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

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 $\left(2y+x\right)^7$

$84y^2x^5$

$280y^3x^5$

$672y^2x^5$

$14y^3x^5$

Pascal's Triangle

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