All You Need To Know about Binomial Theorem 1/2

General Binomial Equation (Given)

binomial formula

Don’t waste memory space trying to remember this, it is given in the formula sheet

Binomial Equation for a specific term

NOT given in the formula sheet … but you can obtain from the general binomial equation given in the formula sheet:

Common Mistakes / Points To Take Note

  • Tn  = “n” th term = Tr+1                         =>         n = r+1
  • Don’t assume the r+1th term Tr+1 is “the term in xr “!

Keywords “term independent of x“ and the constant term” refer to the term : x0.

  • Don’t rush in and waste time expanding the entire expression. Keep the Tr+1 expression in mind when asked to find or compare coefficients of specific terms.

nCr Formula (Given)

(matrix{2}{1}{n r})={n!}/{r!(n-r)!}={n(n-1) cdots (n-r+1)}/{r!}
  • That is not a matrix.

2 Methods to solve for

(matrix{2}{1}{n r})
  1. Press “nCr” button on their calculators
  2. Where n is unknown, it’s worthwhile to be familiar with the following expressions for up till *nC4: (are you able to see a pattern?)
(matrix{2}{1}{n 1})=n/{1!}=n

(matrix{2}{1}{n 2})={n(n-1)}/{2!}
(matrix{2}{1}{n 3})={n(n-1)(n-2)}/{3!}
(matrix{2}{1}{n 4})={n(n-1)(n-2)(n-3)}/{4!}

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