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Binomial Theorem

Binomial Expansion is the expansion (multiplying out) of a
binomial according to its power




(x + y)2

(x + y)3

(x + y)4

(x + y)5



  Some Observations:

  1) Sum of the exponents of each term is equal to the
     power of the binomial

  2) # of terms is always 1 more than the power of the
     binomial

  3) Pattern of the exponents:
    - 1st term of binomial goes down by 1
    - 2nd term of binomial goes up by 1 in expansion
n
Q: If given (x + y) is there an easy way to:
  a) write out the expansion?
  b) find a given term?


  Use the Binomial Theorem
ex. Expand (x + y)7
ex. Expand (x + 2y)5
Day 9 examples

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Day 9 examples

  • 1. Binomial Theorem Binomial Expansion is the expansion (multiplying out) of a binomial according to its power (x + y)2 (x + y)3 (x + y)4 (x + y)5 Some Observations: 1) Sum of the exponents of each term is equal to the power of the binomial 2) # of terms is always 1 more than the power of the binomial 3) Pattern of the exponents: - 1st term of binomial goes down by 1 - 2nd term of binomial goes up by 1 in expansion
  • 2. n Q: If given (x + y) is there an easy way to: a) write out the expansion? b) find a given term? Use the Binomial Theorem
  • 4. ex. Expand (x + 2y)5