Quiz about Binomial Expansion and Pascal's Triangle

Question 1

Expand the binomial expansion $$\left(2x-y\right)^3$$ .

Accepted Answer

$$8x^3-12x^2y+6xy^2-y^3$$

Answer

$$8x^3-12x^2y-6xy^2-y^3$$

Answer

$$8x^3-6x^2y+6xy^2-y^3$$

Answer

$$8x^3+6x^2y+6xy^2-y^3$$

Question 2

In what term is $$x^2$$ located, given the binomial expansion $$\left(x-\frac{1}{x}\right)^8$$ .

Accepted Answer

4th term

Answer

3rd term

Answer

2nd term

Answer

5th term

Question 3

What is the numerical coefficient of the 5th term in the binomial expansion $$\left(3z-\frac{2}{z}\right)^7$$

Accepted Answer

15120

Answer

-22680

Answer

-6048

Answer

1344

Question 4

What is the sum of the numerical coefficients in the expansion $$\left(5a-\frac{3}{b}\right)^7$$

Accepted Answer

128

Answer

24

Answer

48

Answer

256

Question 5

Expand the binomial expansion $$\left(2c-\frac{4}{d}\right)^5$$ .

Accepted Answer

$$32c^5-\frac{320c^4}{d}+\frac{1280c^3}{d^2}-\frac{2560c^2}{d^3}+\frac{2560c}{d^4}-\frac{1024}{d^5}$$

Answer

$$32c^5+\frac{320c^4}{d}+\frac{1280c^3}{d^2}+\frac{2560c^2}{d^3}+\frac{2560c}{d^4}+\frac{1024}{d^5}$$

Answer

$$32c^5-\frac{320c^4}{d}-\frac{1280c^3}{d^2}-\frac{2560c^2}{d^3}-\frac{2560c}{d^4}-\frac{1024}{d^5}$$

Answer

$$32c^5+\frac{320c^4}{d}-\frac{1280c^3}{d^2}-\frac{2560c^2}{d^3}+\frac{2560c}{d^4}-\frac{1024}{d^5}$$

Question 6

Find the missing term in the binomial expansion $$\left(3t-\frac{4}{\sqrt[]{p}}\right)^5=-\frac{1620t^4}{p^{\frac{1}{2}}}+\frac{4320t^3}{p}\ \ \ \ \ \ \ \ \ \ _{ }+\frac{3840t}{p^2}-\frac{1024}{p^{\frac{5}{2}}}+243t^5\ $$

Accepted Answer

$$-\frac{5760t^2}{p^{\frac{3}{2}}}$$

Answer

$$\frac{5760t^2}{p^{\frac{3}{2}}}$$

Answer

$$\frac{1920t^2}{p^{\frac{3}{2}}}$$

Answer

$$-\frac{1920t^2}{p^{\frac{3}{2}}}$$

Question 7

Find the constant term in the expansion $$\left(2w^3-\frac{5}{w^2}\right)^5$$ .

Accepted Answer

-5000

Answer

32

Answer

-400

Answer

2000

Question 8

What is the sum of the coefficient in the 8th row of the Pascal's Triangle?

Accepted Answer

128

Answer

64

Answer

256

Answer

512

Question 9

Find the term which contains $$x^6y^2$$ . Given the binomial expansion $$\left(x^2+3y\right)^5$$ .

Accepted Answer

$$90x^6y^2$$

Answer

$$15x^6y^2$$

Answer

$$270x^6y^2$$

Answer

$$405x^6y^2$$

Question 10

What is the fifth term of the binomial expansion $$\left(3x-4\right)^4$$ .

Accepted Answer

256

Answer

-64

Answer

42

Answer

-12

Binomial Expansion and Pascal's Triangle

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics