Week 17, Day 1

This week we continued our review of topics that will be tested on our final. 
Cristian Vera presented lesson 9.5: Binomial Theorem and Expansion.
When you write out the coefficients for a binomial that is raised to a power, you are expanding a binomial. There are two methods of expansion, both of which provide binomial coefficients. The first is Binomial Theorem, which states that in the expansion of 

(x + y)^n: (x + y) ^n = x^n + (nx^n-1)y +...+ (n)C(r) (x^n-r)y^r +...+ nxy^n-1 + y^n.The coefficient of (x^n-r)y^r is given by a procedure known as combination: (n)C(r) = n! / (n-r)!r!. The second is Pascal's Triangle, in which the first andlast number in each row is 1. Every other number in each row is formed by adding the two numbers immediately above the number. A basic illustration of Pascal's triangle is:

To expand a binomial, it is easiest to use Pascal's Triangle as shown below in an example I got from my original post on the topic:

Because the exponent of the binomial is 6, you would use the 6th row of the triangle. Using the given coefficients, write each appropriate term, and simplify.