The Binomial Theorem
A binomial is a polynomial that has two terms. The Binomial Theorem explains how to raise a binomial to certain non-negative power.
The theorem states that in the expansion of ,
, the coefficient of is
The symbol is often used in place of to denote binomial coefficient.
The expansion is expressed in the sigma notation as .
Note that, the sum of the degrees of the variables in each term is .
What is the coefficient of in the expansion of .
Use the binomial theorem to determine the general term of the expansion.
The general term in the expansion of is .
Here, , and . The term that has the fourth power of the variable will be the fourth term in the expansion. Therefore, substitute in the binomial coefficient of the general term and evaluate.
Therefore, the coefficient of in the expansion is .