In this video I work an example problem on binomial expansion.
Video 1 Binomial Expansion
In the example I'm expanding a binomial with a negative term.
We will use Pascal's triangle and it starts with 1 then 1 1 and then 131 and 1331. As you move down Pascal's triangle it is to the 0 degree then to the first,then squared,then cubed.
The coefficients will be 1 3 3 1 because it is cubed.
I end up with,
(2x)3 (2x)2 (2x)1 (2x)0
The next term of the binomial I will ascend because it is negative.
The numbers will be to the zero power,then first power,then second, then cubed.
As you expand each term will have an exponent with a sum of three because you are expanding a cubic.
Finally you combine the columns
Another rule to keep in mind is the n+1
Because you are expanding a cube, you take 3+1 so you will have 4 terms when expanding the binomial
This is the n+1 rule.
Also when you are expanding a binomial with subtraction,every other term will be negative.
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Tagged under: math,binomial expansion,Pascal' triangle,binomial theorem,binomial distribution,binomial expansion pascal triangle,expand pascal' triangle,binomial,binomial negative term
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