Search Header Logo
Multinomial Expansion Concepts

Multinomial Expansion Concepts

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial introduces the multinomial theorem, explaining its statement and application. It provides a detailed example of expanding (X + Y + Z)^4 using the theorem, demonstrating how to calculate coefficients and systematically list all terms. The tutorial concludes with a method to find specific coefficients in the expansion.

Read more

9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the multinomial theorem help to expand?

A product of two binomials

A quadratic equation

A sum of multiple variables raised to a power

A single variable polynomial

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the multinomial theorem, what is the constraint on the indices?

They must sum to n

They must be prime numbers

They must sum to zero

They must all be equal

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are multinomial coefficients used for?

To calculate the coefficients in a multinomial expansion

To solve linear equations

To determine the number of terms in an expansion

To find roots of polynomials

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the example (X + Y + Z)^4, what is the sum of the indices i, j, and k?

4

3

5

6

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of re-indexing terms in the multinomial expansion?

To increase the power

To change the variables

To reduce the number of terms

To simplify the calculation

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you determine the number of possible terms in a multinomial expansion?

By counting the variables

By listing all combinations of indices that sum to n

By using the power of the expansion

By dividing the power by the number of variables

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the coefficient of the term x^3y in the expansion of (X + Y + Z)^4?

4

6

12

24

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?