Intermath | Workshop Support


The 26th Degree / FOIL Frenzy 

Problem Statement
What is (x-a)(x-b)(x-c)...(x-y)(x-z)? 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 3rd 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 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.

Author & Contact
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