Binomial Expansion | Pascal's Triangle | How to Expand a Binomial that is Raised to an Exponent

Binomial expansion is the procedure of expanding a binomial that is raised to an exponent. It consists of the following steps:
1. Write the expressions for the terms
Pattern: The first term in the expansion is the product of the first term (say x) of the given binomial raised to the given exponent and the second term (say y) of the given binomial raised to the exponent zero. For the succeeding terms, we have to subtract 1 from the exponent of x while adding 1 to the exponent of y. Take note that the sum of exponents in each term in the expansion should be equal to the given exponent.
2. Determine the signs of the terms
Two Cases:
a. Operation in the given binomial is addition - all terms in the expansion are positive
b. Operation in the given binomial is subtraction - the terms in the expansion are alternately positive and negative (Note: The first term in the expansion is always positive)
3. Determine the coefficients (numbers that are multiplied to the expressions) of the terms using the Pascal's Triangle
4. Simplify the terms