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 September 23rd, 2017, 02:31 AM #1 Newbie   Joined: Sep 2017 From: UK Posts: 1 Thanks: 0 Order of Operations comprehension question Hello, this is my first post here, so please go easy on me! Thank you for your time. As far as I understand: if $\displaystyle x = a + b$ then $\displaystyle x^{2} = (a + b)^{2}$ not $\displaystyle x^{2} = a^{2} + b^{2}$ which I can easily check by asking does $\displaystyle 5^{2} = 3^{2} + 2^{2}$? No. My question is does anyone have a way of explaining this property so that I might better understand *why* this property exists, beyond simply memorising it as a property of algebra? The reason I ask is because sometimes I make this mistake in algebraic manipulations; a specific example would be from physics: since $\displaystyle v = u + at$ $\displaystyle v^{2} = (u + at)^{2} = u^{2} + 2at + a^{2}t^{2}$ However, if I am not careful, in practise I have previously resolved this as: $\displaystyle v^{2} = u^{2} + a^{2}t^{2}$, since in my mind I am "just squaring both sides." So my request is if anyone could give me an understanding to help cement this algebraic rule in my mind in a deeper way, so I don't make this mistake again. I hope that's clear. Thanks in advance for any insight. Sam October 1st, 2017, 02:15 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,131 Thanks: 2339 $(a + b)^2 = (a + b)(a + b) = a(a + b) + b(a + b) = a*a + ab + b*a + b*b = a^2 + 2ab + b^2$ October 1st, 2017, 02:20 AM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,849 Thanks: 661 Math Focus: Yet to find out. This mistake has a name of its own! See here. https://en.m.wikipedia.org/wiki/Freshman%27s_dream October 1st, 2017, 04:12 AM   #4
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Quote:
 Originally Posted by sdparsons since $\displaystyle v = u + at$ $\displaystyle v^{2} = (u + at)^{2} = u^{2} + 2at + a^{2}t^{2}$
Should be: = u^2 + 2uat + a^2t^2

Code:
 2 + 3
2 + 3
-------
6 + 9 : do bottom "3" next
-----------
4 +12 + 9 = 25
There's really 2 multiplications:
2 * (2 + 3), then 3 * (2 + 3) Tags comprehension, operations, order, question 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 GOAT Algebra 7 October 11th, 2014 09:51 AM Doogz Elementary Math 4 December 9th, 2012 02:14 PM daigo Algebra 1 May 17th, 2012 03:59 PM buddy8756 Algebra 16 April 7th, 2011 10:55 PM melorock089 Calculus 2 September 22nd, 2009 05:36 AM

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