Understanding Binomial Expansion Coefficients

The video tutorial explains the concept of binomial coefficients, focusing on how to determine the coefficient of specific terms in binomial expansions. It starts with a basic example using simple binomials and progresses to more complex cases involving non-unit coefficients and negative terms. The tutorial emphasizes the importance of understanding the relationship between the terms and coefficients in binomial expansions.

What is the coefficient of x^3y^5 in the expansion of (x + y)^8?

• 28

• 56

• 70

• 84

In a simple binomial expansion, what does 'n choose k' represent?

• The product of the exponents

• The coefficient of a term

• The sum of the exponents

• The difference of the exponents

How do you determine the coefficient of x^7 in the expansion of (x + 3)^12?

• 12 choose 3

• 12 choose 5

• 12 choose 9

• 12 choose 7

What is the value of 3^5 in the expansion of (x + 3)^12?

• 81

• 1024

• 243

• 729

In the expansion of (x + 3)^12, what is the coefficient of x^7?

• 100,000

• 243,000

• 192,456

• 150,000

What is the coefficient of x^5 in the expansion of (2x - 3)^8?

• -48,384

• 48,384

• -32,000

• 32,000

In the expansion of (2x - 3)^8, what is the value of 2^5?

• 64

• 32

• 16

• 128

What is the value of (-3)^3 in the expansion of (2x - 3)^8?

• 27

• 81

• -81

• -27

In the expansion of (2x - 3)^8, what is the combination used to find the coefficient of x^5?

• 8 choose 2

• 8 choose 7

• 8 choose 5

• 8 choose 3

What is the general formula for finding the coefficient of a term in a binomial expansion?

• n choose k times x^k times y^n

• n choose k times x^n times y^k

• n choose k times x^(n-k) times y^k

• n choose k times x^k times y^(n-k)