Binomial Expansion and Coefficients

Binomial Expansion and Coefficients

Assessment

Interactive Video

Mathematics, Science, Computers

9th - 10th Grade

Practice Problem

Hard

Created by

Patricia Brown

FREE Resource

The video tutorial explains how to find the sixth term in the expansion of (X - 2Y)^10 using the binomial theorem. It covers the use of combinations and calculations to determine the term, emphasizing the importance of understanding the powers and coefficients involved. The tutorial concludes with the final calculation, resulting in the term -8064.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main problem discussed in the video?

Calculating the derivative of a function

Finding the area under a curve

Finding the sixth term in the expansion of (X - 2y)^10

Solving a quadratic equation

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which mathematical tools are mentioned for solving the problem?

Matrix multiplication

Trigonometric identities

Differential equations

Pascal's Triangle and the Binomial Theorem

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does 'nCr' represent in the context of the Binomial Theorem?

The sum of n and r

A combination of n items taken r at a time

The difference between n and r

The product of n and r

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many times would you need to multiply (X - 2y) by itself to expand it to the 10th power?

15 times

10 times

5 times

20 times

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the power of X in the sixth term of the expansion?

4

6

10

5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What should the sum of the powers of X and Y be in each term of the expansion?

10

5

20

15

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the power of Y in the sixth term of the expansion?

10

4

6

5

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