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 September 19th, 2018, 12:24 PM #1 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Hmmm... n^4 - n^3 + n^2 - n = n*{n*[n*(n - 1) + 1] - 1} Just got that...kinda accidentally...mean anything?
September 19th, 2018, 01:06 PM   #2
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Quote:
 Originally Posted by Denis n^4 - n^3 + n^2 - n = n*{n*[n*(n - 1) + 1] - 1} Just got that...kinda accidentally...mean anything?
It means you expanded the right side of the equation?

 September 19th, 2018, 02:43 PM #3 Newbie   Joined: Jul 2018 From: Georgia Posts: 28 Thanks: 7 Okay, I was being mildly facetious in my first reply. I would like to know how you happened upon that. If you expand from the inside out, starting with what's inside the square brackets, you have: n^2 - n + 1 Next step out - the curly brackets: n^3 - n^2 + n - n And that's the key step. You've got the +n and -n, which are already zero if you're going to do anything else to that entire string. So the key to this seems to be including +1 inside the square brackets, but external to the parentheses, and then including -1 inside the curly brackets but external to the square brackets. Since you're essentially multiplying each 'group'' successively by n, then you've guaranteed producing a +n and a -n by that setup. Was there something else there that you saw or wondered about?
September 19th, 2018, 02:52 PM   #4
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Quote:
 Originally Posted by Denis n^4 - n^3 + n^2 - n = n*{n*[n*(n - 1) + 1] - 1} Just got that...kinda accidentally...mean anything?
But that means you are squaring n by doing n*n!!

-Dan

September 19th, 2018, 03:28 PM   #5
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Quote:
 Originally Posted by RichardJ Was there something else there that you saw or wondered about?
Don't lose any sleep Dick: was simply screwing around...

 September 19th, 2018, 04:15 PM #6 Senior Member   Joined: Sep 2016 From: USA Posts: 645 Thanks: 407 Math Focus: Dynamical systems, analytic function theory, numerics I'm not sure if this is just satirizing the other thread but this formula is actually quite useful. The RHS is how you would evaluate the polynomial, $n^4 - n^3 + n^2 - n$ using Horner's algorithm. If you haven't seen it before its pretty simple but very powerful. https://en.wikipedia.org/wiki/Horner%27s_method Thanks from greg1313
 September 19th, 2018, 06:28 PM #7 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond I knew that had a name - couldn't think of it though.

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