The 26th Degree / FOIL Frenzy
(x-a)(x-b)(x-c)...(x-y)(x-z)? Explain how you found the answer.
In this problem I will be multiplying
26 binomials together to determine the product.
Solve/Investigate the Problem
I will begin by multiplying the
first 2 binomials together.
Then I will multiply the result by the 3rd binomial and
so on until I have multiplied all 26 binomials together.
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 3rd
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 226, or 67,108,864 terms. This
did not appear to be a feasible task.
Upon further exploration I
discovered that the 24th binomial was (x-x). What
a break! (x-x) = 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 226 is equal to 67,108,864, what is 227? The final answer is 134,217,728.
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