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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: 21,019 Thanks: 2252 (a + b + c + d)� ? a� + b� + c� + d� + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd June 11th, 2013, 02:48 AM   #3
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Re: Formulae Required

Quote:
 Originally Posted by qamath09 What is the formula for (a+b+c+d)^2 . Please help
Well, you're going to get

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 a�+ab+ac+ad+ba+b�+...+cd+d�. Simplifying gives a� + b� + c� + d� + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd. So (a + b + c + d)^2 = a� + b� + c� + d� + 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: 2,298 Thanks: 959 Math Focus: Wibbly wobbly timey-wimey 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)� => ( (a+b) + (c+d) )� => (a+b)� + (c+d)� + 2(a+b)(c+d) => a� + b� + 2ab + c� + d� + 2cd + 2 (ac + bc + ad + bd) => a� + b� + c� + d� + 2ab + 2cd + 2ac + 2bc + 2ad + 2bd (a+b)� = a� + b� + 2ab Tags formulae, required Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Bogauss Number Theory 18 August 15th, 2016 03:49 PM apvkt Algebra 1 October 26th, 2012 09:42 PM chocolate Algebra 4 June 8th, 2012 06:05 PM randomFire Algebra 6 February 1st, 2011 12:17 AM skylineview945r2 Algebra 5 January 9th, 2011 04:23 PM

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