How do you use the binomial series to expand #(1 + x)^12#?
1 Answer
Explanation:
The Binomial Theorem is a very useful tool that gives us a way to find the coefficients of binomials raised to some power

Pascal's Triangle: This is the easiest way, but also only useful if you have a copy of the triangle on hand. If you do, look at row 12 (remember the top is row 0) and use the coefficients from that row.

The Choose Function: This method actually comes from the theorem itself. The function basically says how many ways there are to choose
#r# items from a group of#n# objects where order does not matter.
Turns out this function can predict binomial coefficients too. You can find them using the#n"C"r# function on your calculator where#n=12# and#r# is increasing from#0 12# . 
Factorials: Should your calculator not have an
#n"C"r# function, you can evaluate the function directly using factorials (#!# ). The factorial of a whole number is that number multiply by all other whole numbers between#1# and itself. The formula for the choose function is:
#n"C"r = (n!)/(r!(nr)!)# where#r# and#n# have the same meaning as before.
No matter how you get the coefficients, the answer will still be the same:
Notice how as the power of