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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
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Re: Simplifying this equation

Hello, Kinh!

Do you know how to square a binomial?

$(3u\,+\,3v)^2 \:=\:(3u\,+\,3v)(3u\,+\,3v) \:=\:9u^2\,+\,9uv\,+\,9uv\,+\,9v^2 \:=\:9u^2\,+\,18uv\,+\,9v^2$

$3(u\,-\,v)^2 \:=\:3(u^2\,-\,2uv\,+\,v^2) \:=\:3u^2\,-\,6uv\,+\,3v^2$

Quote:
 Can anyone please show me how to solve this equation? [color=beige]. . [/color]$(3u\,+\,3v)^2\,-\,3(u\,-\,v)^2$

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]$(3u\,+\,3u)^2\,-\,3(u\,-\,v)^2$

[color=beige]. . . . . [/color]$=\;(9u^2\,+\,18uv\,+\,9v^2) \,-\,(3u^2\,-\,6uv\,+\,3v^2)$

[color=beige]. . . . . [/color]$=\;9u^2\,+\,18uv\,+\,9v^2\,-\,3u^2\,+\,6uv\,-\,3v^2$

[color=beige]. . . . . [/color]$=\;6u^2\,+\,24uv\,+\,6v^2$

 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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