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November 13th, 2013, 11:26 AM  #1 
Newbie Joined: Nov 2013 Posts: 1 Thanks: 0  Help!! A.s.a.p. I'm really confused!
I'm doing my maths homework and I don't understand this question! I don't know how to do the small 3 or 2, the ones that are powers like 3 to the power of 2 is 3x3=9. So when I write to the power of, you will know what I mean hopefully. For any even number n, prove that the product of it and the next two consecutive even numbers will be n to the power of 3 + 6n to the power or 2 + 8n That is the question in my maths textbook and I can't find anything anywhere to help me! If someone could please give me the answer and explain how they got it, that would be brilliant! Please+Thankyou!!! 
November 13th, 2013, 11:54 AM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Help!! A.s.a.p. I'm really confused!
Do you mean: show that: 
November 13th, 2013, 01:38 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,505 Thanks: 1741 
n(n + 2)(n + 4) = n(n(n + 4) + 2(n + 4)) = n(n² + 4n + 2n + 8) = n³ + 6n² + 8n (Pero omitted the final n.) The equation holds for any value of n; n needn't be an even number and needn't be an integer. The need for n to be an even integer is caused purely by the wording "next two consecutive even numbers" used in the description of the equation. 

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