|
|
The Binomial Theorem
|
The binomial theorem, sigma notation
and binomial expansion
algorithm |
The
binomial theorem and binomial expansion algorithm examples |
|
|
|
|
|
The binomial theorem, sigma notation
and binomial expansion
algorithm |
The
theorem that shows the form of the expansion of any positive integral
power of a binomial (a
+ b)n
to a polynomial with n
+ 1 terms, |
![](BinomialTheorem.gif) |
|
The
binomial theorem and binomial expansion algorithm examples
|
|
|
Example: Find
the 4th term of the binomial
expansion (a - x)5. |
|
Or,
we can use the formula to find (k
+ 1)th
term. |
|
|
Since, n =
5
and k
+ 1 = 4 =>
k
=
3
then by plugging these values into |
![](BinomialEx2a.gif) |
|
![](BinomialEx2b.gif) |
|
Example: Find
the middle
term of the binomial
expansion |
![](BinomialEx3.gif) |
|
|
|
Example: Find
the 7th term of the binomial
expansion |
![](BinomialEx4.gif) |
if the coefficient of the third
term |
|
relates
to the coefficient of the second term as 9 : 2. |
|
|
Example:
Which term of the binomial
expansion |
![](BinomialEx5.gif) |
is missing x? |
|
|
To
fulfill the required condition, the exponent of x
must be zero, therefore |
![](BinomialEx5b.gif) |