Testwiki:Reference desk/Archives/Mathematics/2011 August 23

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August 23

Multiplying a Factorial by Another Factorial

When it comes to dividing a factorial by another factorial, you can "cancel" them out. But when multiplying a factorial by another factorial, is there a shortcut there too, or is it just figure out what factorials are, then multiply them? --Thebackofmymind (talk) 10:10, 23 August 2011 (UTC)

Your question is like the following: When it comes to dividing an X by another X, you can "cancel" them out. But when multiplying an X by another X, is there a shortcut there too, or is it just figure out what X-s are, then multiply them?

Hope this helps.

HOOTmag (talk) 10:25, 23 August 2011 (UTC)

The only identity I can think of, for m>n, is $n!m!=(n!{)}^2(m\cdot (m-1)\cdot ...\cdot (n+1))$, that may or may not make the mental calculation easier. Widener (talk) 11:20, 23 August 2011 (UTC)

So, for example, 9! × 11! = (9!)² × 10 × 11. StuRat (talk) 09:19, 24 August 2011 (UTC)

Factorization

Help me factorize X squared + 4x + 3 + mx + 3m — Preceding unsigned comment added by Agdesi (talk • contribs) 15:02, 23 August 2011 (UTC)

Here is a hint: gather terms in the same power of x together and rewrite the expression as

$x^2+(m+4)x+3(m+1)$

Gandalf61 (talk) 15:05, 23 August 2011 (UTC)

Also, try to group the "unknowns" into a similar format, as in $x^2+((m+1)+3)x+3(m+1)$. Now, "m+1" is in both terms containing m. -- kainaw™ 16:15, 23 August 2011 (UTC)

Why the long tail is just a 2 variables graph and not a 3 variables graph??

You have the amount or % of the different products being sold. The amount of % of population. And the amount or % of products sold. So you have 3 variables, but use a 2d graph to explain long tail.201.78.194.18 (talk) 20:54, 23 August 2011 (UTC)

Have you looked at the long tail article? It's all explained there. — Fly by Night (talk) 21:51, 23 August 2011 (UTC)