Understanding Binomial Coefficients

This video tutorial explains binomial coefficients, which are the coefficients in the expanded form of a binomial expression. It covers the expansion of binomials for various powers, demonstrating the process of multiplying and collecting like terms. The tutorial also introduces a more efficient method for determining binomial coefficients using combinations, illustrated with examples. The video concludes with practical applications of these concepts, including finding specific coefficients in binomial expansions.

What is the value of any non-zero number raised to the power of zero?

• One

• Undefined

• Zero

• The number itself

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CCSS.HSA.APR.C.4

When expanding the square of a binomial, which method involves distributing each term of the first binomial across the second?

• Triple distribution

• Double distribution

• FOIL method

• Single distribution

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CCSS.HSA.APR.C.5

What is the coefficient of x^3y^2 in the expansion of (x + y)^5?

• 5

• 10

• 20

• 15

Tags

CCSS.HSA.APR.C.5

How do you determine the number of bit strings of length n with weight k?

• n choose k

• k choose n

• k times n

• n times k

Tags

CCSS.HSA.APR.C.5

In the expansion of (x + y)^5, what is the coefficient of x^2y^3?

• 5

• 15

• 10

• 20

Tags

CCSS.HSA.APR.C.5

What is the coefficient of x^7y^5 in the expansion of (x + y)^12?

• 1200

• 1001

• 924

• 792

Tags

CCSS.HSA.APR.C.5

In the expansion of (x + 2)^15, what additional step is needed compared to (x + y)^n?

• Multiply by 2^15

• Multiply by 2^5

• Multiply by 2^10

• No additional step

Tags

CCSS.HSA.APR.C.5

What is the coefficient of x^10 in the expansion of (x + 2)^15?

• 3003

• 15015

• 96096

• 32768

Tags

CCSS.HSA.APR.C.5

In the expansion of (x + 2)^15, what is the value of 2 raised to the power of 5?

• 16

• 32

• 128

• 64

Tags

CCSS.HSA.APR.C.5

What is the sum of the exponents in any term of the expansion of (x + y)^n?

• 2n

• n+1

• n-1

• n

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CCSS.HSA.APR.C.5