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March 8th, 2014, 05:17 AM   #1
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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.
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March 8th, 2014, 05:21 AM   #2
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Re: Simplifying this equation

Sorry, the font size didn't work for some reason.
It's...
(3u + 3v) - 3(u - v)
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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?





Quote:
Can anyone please show me how to solve this equation?
[color=beige]. . [/color]

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]

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March 8th, 2014, 06:41 PM   #4
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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?
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March 10th, 2014, 12:55 AM   #5
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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 - (3u - 6uv + 3v) with - (3u + 6uv - 3v).
It was replaced with -3u + 6uv - 3v.

The final answer of 6u + 24uv + 6v could be written as 6(u + 4uv + v). Authors may disagree as to which form is simpler.
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March 13th, 2014, 11:00 PM   #6
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(3u + 3v) - 3(u - v) = (9u + 18uv + 9v) - 3(u - 2uv + v) = 9u + 18uv + 9v - 3u + 6uv - 3v = 6u + 24uv + 6v
6u + 24uv + 6v = 6(u + 4uv + v)
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