Title
The 26^{th} Degree / FOIL Frenzy
Problem Statement
What is
(xa)(xb)(xc)...(xy)(xz)? Explain how you found the answer.
Problem setup
In this problem I will be multiplying
26 binomials together to determine the product.
Plans to
Solve/Investigate the Problem
I will begin by multiplying the
first 2 binomials together.
Then I will multiply the result by the 3^{rd} binomial and
so on until I have multiplied all 26 binomials together.
Investigation/Exploration
of the Problem
I began by multiplying the
first 2 binomials together using the FOIL
method. I noticed that the product produced had 4 terms. After multiplying by the 3^{rd}
binomial, I noticed that the product produced 8 terms. Upon further exploration I began
seeing a pattern emerge between the number of binomial factors and powers
of 2. I determined that the
final product would contain 2^{26}, or 67,108,864 terms. This
did not appear to be a feasible task.
Upon further exploration I
discovered that the 24^{th} binomial was (xx). What
a break! (xx) = 0.
Thanks to the zero property of multiplication my
problem was solved. Zero times
anything is zero.
My final answer: 0.
Extensions of the Problem
If 2^{26} is equal to 67,108,864, what is 2^{27}? The final answer is 134,217,728.
Author & Contact
Insert name and contact information.
lparsons@rockdale.k12.ga.us
Link(s) to resources, references, lesson plans, and/or other
materials
Link 1
Link 2
U
Important Note: You should compose your writeup
targeting an audience in mind rather than just the instructor for the
course.
You are creating a page to publish it on the web.
