

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, 


The
binomial theorem and binomial expansion algorithm examples



Example: Find
the 4^{th} 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 




Example: Find
the middle
term of the binomial
expansion 




Example: Find
the 7^{th} term of the binomial
expansion 

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 

is missing x? 


To
fulfill the required condition, the exponent of x
must be zero, therefore 









College
algebra contents
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