Use the binomial theorum to expand (x - 2y)^8.

 Aug 28, 2020

Assuming you know what the binomial theorem is...(tap the link, if you dont know, and go to the section that says "statement")


We could just use the binomial theorem to expand right away, but that would be not so smart, as the number "8" is considered small enough to be calculated with this picture:




We can see already factored out coefficients on the 9th row! Isn't that just awesome...?


All that being said, we can start! 


If we just used (x + y)^8 to start, we see that this expands out to: 



using the binomial theorem and the triangle, formally known as "Pascal's Triangle".


But, instead of y, we have -2y... so what do we do? Simple: we just plug that in for y! This will become:



There! An answer that you can't just copy and paste, isn't that awesome??? Anyways, here is a 3D graph for geeks:







Citations: All images generated with WolframAlpha graphing

 Aug 28, 2020
edited by ilorty  Aug 28, 2020

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