Objectives:
  • Understand and use Pascal's Triangle and/or the notation (n r) to find the binomial coefficient of any term
  • Understand and use the binomial theorem to expand (1 + b)^n, (a + b)^n for n>0.
  • Understand and use T(n+1)=(n r)a^(n-r)b^r to find a particular term.

Resources: Marshall Cavendish TB Ch 5
Notes:

Powerpoint Slides - for those who like it step-by-step...


For download:

Educational Videos - for those who prefer hearing someone talking :)

Pascal's Triangle
Watch this video to see how the Pascal's Triangle can be generated and how interesting patterns can be found in it.

[URL: http://www.youtube.com/watch?v=YUqHdxxdbyM&feature=related]

Use of Pascal's Triangle to generate the binomial coefficients:

[URL: http://www.youtube.com/watch?v=OMr9ZF1jgNc&feature=fvw]

The definition of (n r):
*Accent a little hard to follow, need some patience

[URL: http://www.youtube.com/watch?v=swbSsQsrBRE&feature=related]

The Binomial Expansion - making expansion of binomial terms easier:

[URL: http://www.youtube.com/watch?v=h3wdStMSfXk&feature=channel]

More on using the Binomial Expansion for (a+b)^n, a not =1:

[URL: http://www.youtube.com/watch?v=7unrasRNZnY&feature=channel]

More Examples of how to apply the binomial theorem:

[URL: http://www.youtube.com/watch?v=1pSD8cYyqUo&feature=channel]

More Examples of how to apply the binomial theorem:

[URL: http://www.youtube.com/watch?v=TeE-ypKj8ZI&feature=channel]

Finding the coefficient of a particular term:

[URL: http://www.youtube.com/watch?v=ktDy4ExrctQ&feature=channel]


Binomial Theorem textbook practice:
Pg 118 Ex 5.1 Q4, 5, 7, 8, 11, 13, 16, 17
Pg 124 Ex 5.2: Q3, 5, 6, 7, 11, 15, 17, 20, 21, 22
Pg 127 Revision Ex 5 B2


Solutions to Textbook Exercises: