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June 11th, 2013, 02:38 AM  #1 
Newbie Joined: Jun 2013 Posts: 2 Thanks: 0  Formulae Required
What is the formula for (a+b+c+d)^2 . Please help

June 11th, 2013, 02:47 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,809 Thanks: 2150 
(a + b + c + d)² ? a² + b² + c² + d² + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd

June 11th, 2013, 02:48 AM  #3  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Formulae Required Quote:
a^2 + b^2 + c^2 + d^2 ... that's easy... then every multiplicative combination of 2 letters twice... from left to right you will get ab + ac + ad + bc + bd + cd twice, so finally, a^2 + b^2 + c^2 + d^2 + 2(ab + ac + ad + bc + bd + cd)  
June 11th, 2013, 03:45 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Formulae Required (image not to scale) The surface of the square is the product of the length of the sides. (a + b + c + d) * (a + b + c + d) = (a + b + c + d)^2. The surface of the square is also the sum of the surfaces of all the smaller rectangles. Which is a²+ab+ac+ad+ba+b²+...+cd+d². Simplifying gives a² + b² + c² + d² + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd. So (a + b + c + d)^2 = a² + b² + c² + d² + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd. Note: every square is also a rectangle so even if for example a = c, then ac can still be called rectangle. 
June 11th, 2013, 06:18 AM  #5 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,226 Thanks: 908 Math Focus: Wibbly wobbly timeywimey stuff.  Re: Formulae Required
Or, by the distributive property: etc. Dan 
June 11th, 2013, 07:12 AM  #6 
Member Joined: May 2013 From: Phnom Penh, Cambodia Posts: 77 Thanks: 0  Re: Formulae Required
(a+b+c+d)^2 =(a+b)^2 +(c+d)^2 +2(a+b)(c+d) =a^2 +b^2 +c^2 +d^2 +2(ab+bc+cd+da+ac+bd). 
June 11th, 2013, 10:18 PM  #7 
Newbie Joined: Jun 2013 Posts: 1 Thanks: 0  Re: Formulae Required
(a+b+c+d)² => ( (a+b) + (c+d) )² => (a+b)² + (c+d)² + 2(a+b)(c+d) => a² + b² + 2ab + c² + d² + 2cd + 2 (ac + bc + ad + bd) => a² + b² + c² + d² + 2ab + 2cd + 2ac + 2bc + 2ad + 2bd (a+b)² = a² + b² + 2ab 

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