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Binomial Theorem and Expansions

Expansion of binomials raised to a power using combinations.

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Combinations and the Binomial Theorem

Vocabulary

Complete the chart.
Word Definition
Combination ____________________________________________________________
Factorial ____________________________________________________________
Binomial Theorem ____________________________________________________________
_______________ the process of raising a binomial such as (x + 2) to a power
_______________ a pyramid of sorts constructed with the coefficients of binomials as they are expanded

Factorials and Combinations

Expand n!= ___________________________________

Simplify and Evaluate the Factorials:

  1. (a+3)!(a+4)!
  2. 5!4!2!
  3. 11!7!

Solve

  1. 9C7
  2. 5C2
  3. The local TV station forecasts a 14% chance of rain every day for the next week. What is the probability that it will rain on exactly 4 out of the next 7 days?

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Binomial Theorem and Expansions

Pascal's Triangle can help expand binomials. 

It follows the pattern (nr1)+(nr)=(n+1r) .

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When you expand ( x + y ) n , the exponents of x ______________ whille the exponents of y ______________. 

What is the Binomial Theorem in summation form? _________________________

Explain how finding a term in an expansion can be used to answer a particular kind of probability question. _____________________________________________________________________________________________________________________________________________

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  1. Expand: (3x+a)5
  2. Expand: (xy)7
  3. Expand: (2x+3)4
  4. Find the 5th term in the expansion (4x3a)9 .
  5. What is the coefficient of x5 in the expansion of (3x+4)6 ?

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