Binomial Theorem: Expansion
View the Lesson | MATHguide Homepage Updated May 4th, 2017


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Given:
(a + b)7 = 7C0a7 + 7C1a6b + 7C2a5b2 + 7C3a4b3 + 7C4a3b4 + 7C5a2b5 + 7C6ab6 + 7C7b7
 
Expand:
(2x - 3)7
 
Section 1: First, substitute values for coefficients, the a-value, and the b-value.
(2x - 3)7 =
  1st term:(x)7
  2nd term:(x)6()
  3rd term:(x)5()2
  4th term:(x)4()3
  5th term:(x)3()4
  6th term:(x)2()5
  7th term:(x)()6
  8th term:()7
 
Section 2: Next, write the correct final coefficients.
(2x - 3)7 =
x7 + x6 + x5 + x4 + x3 + x2 + x +