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March 8th, 2014, 05:17 AM  #1 
Newbie Joined: Mar 2014 Posts: 19 Thanks: 0  Simplifying this equation
Can anyone please show me how to solve this equation? (3u + 3v)2  3(u  v)2 I just can't work out the process in breaking it down. I tried multiplying each parentheses into each other and still it doesn't work. Thanks. 
March 8th, 2014, 05:21 AM  #2 
Newbie Joined: Mar 2014 Posts: 19 Thanks: 0  Re: Simplifying this equation
Sorry, the font size didn't work for some reason. It's... (3u + 3v)²  3(u  v)² 
March 8th, 2014, 08:04 AM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Simplifying this equation Hello, Kinh! Do you know how to square a binomial? Quote:
First of all, "solve this equation" is incorrect.[color=beige] .[/color]There is no equation. You want to simplify the expression. From my preliminary work above: [color=beige]. . [/color] [color=beige]. . . . . [/color] [color=beige]. . . . . [/color] [color=beige]. . . . . [/color]  
March 8th, 2014, 06:41 PM  #4 
Newbie Joined: Mar 2014 Posts: 19 Thanks: 0  Re: Simplifying this equation
Thanks for that, it helped a lot. I take it the reason why you switched the  and + signs around (with the 2nd parentheses) was because the  multiplied by a number with another  gives that number a positive value, conversely the ,+ together gives a negative. That's where I went wrong. (9u2 + 18uv + 9v2)  (3u2  6uv + 3v2) (9u2 + 18uv + 9v2)  (3u2 + 6uv  3v2) So that minus in between the two parentheses has a value of 1, right? 
March 10th, 2014, 12:55 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 21,020 Thanks: 2256 
It's correct that "" and "1" are equivalent, but it's acceptable not to introduce "1" in your answer, as you can simply distribute "" to each term within the parentheses and remove the parentheses. Note that [color=#00AA00]soroban[/color] didn't replace  (3u²  6uv + 3v²) with  (3u² + 6uv  3v²). It was replaced with 3u² + 6uv  3v². The final answer of 6u² + 24uv + 6v² could be written as 6(u² + 4uv + v²). Authors may disagree as to which form is simpler. 
March 13th, 2014, 11:00 PM  #6 
Senior Member Joined: Mar 2014 Posts: 112 Thanks: 8 
(3u + 3v)²  3(u  v)² = (9u² + 18uv + 9v²)  3(u²  2uv + v²) = 9u² + 18uv + 9v²  3u² + 6uv  3v² = 6u² + 24uv + 6v² 6u² + 24uv + 6v² = 6(u² + 4uv + v²) 

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