T2 HBL
Updated: 4/8/2021
T2 HBL

Storyboard Text

  • n! = n(n-1)(n-2)(n-3) ...
  • Hello class, before we move on to calculus, we have a small topic on Binomial Theorem to cover.
  • BINOMIAL THEOREM
  • (x + y)4 =
  • (x + y)2 =
  • A binomial is a mathematical expression containing two terms. If raised to an integer power, it can be expanded in this manner. Notice how the power of the first variable decreases by 1 when moving from term to term, while that of the second increases.
  • (x + y)3 =
  • 
  • x4 + 4x3y + 6x2y2 + 4xy3 + y4
  • 
  • x3 + 3x2y + 3xy2 + y3
  • x2 + 2xy
  • + y2
  • We can use this array of numbers called the Pascal's triangle, where the row number is the exponent, while the numbers in each row represent the coefficients for the respective terms.
  • 11 2 11 3 3 11 4 6 4 11 5 10 10 5 1
  • This enables us to use the nCr notation, to find the coefficient of the rth term in a binomial, starting from 0, among n terms, which is is always 1 more than the exponent.
  • Alternatively, we are able to obtain the coefficients using another method, which involves the concept of factorials, the product of consecutive descending numbers.
  • nCr =
  • n
  • r
  • ( )
  • =
  • n!
  • r! (n-r!)
  • With these 2 concepts, we can derive the general term of an expanded binomial. This is particularly useful if we just want to identify a particular term in the whole expression.
  • Tr+1 =
  • In (x + y)n ,
  • r
  • n
  • ( )
  • xn-r
  • yr
  • OK class, now take out your A4 paper, we will do some written work, 20 minutes.
  • BINOMIAL THEOREM
  • Oh no!!