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how do i solve this? how can i simplify it?

$(\sqrt{7x} - \sqrt{2y})^2$

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    The usual $x^2-2xy+y^2$ still applies.2011-04-19
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    There is nothing to "solve". You have an expression, not an equation.2011-04-19
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    Did you mean to have it equal to $0$?2011-04-19
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    @Arturo Obviously the OP seeks to solve the problem of simplifying the expression. As a native (US) English speaker, I see no problem using the word solve in such a context.2011-04-19

1 Answers 1

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In general, $(a - b)^2 = a^2 + b^2 - 2ab$. So here, we get that $(\sqrt{7x} - \sqrt{2y})^2 = 7x + 2y -2 \sqrt{14xy}$. Unfortunately, there is nothing to 'solve' since that would require there to be some constraint, e.g. $(\sqrt{7x} - \sqrt{2y})^2 = 0$. But this is a simpler form.

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    how about? (sqrt(2 * y) + sqrt(7 * x)) * (sqrt(7 * x) - sqrt(2 * y)) and answer would be 7x-2y2011-04-19
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    why on the answer it didn't follow the rule a^2 +b^2 - 2ab2011-04-19
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    I dont see 2 before sqrt(14xy)2011-04-19
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    @mr student You are absolutely right! I have edited it to include the 2. Good catch.2011-04-19
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    @mixedmath: The use of "solve" here is fine - see my comment above.2011-04-19
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    @Bill Dubuque: While I might say that as an English speaker, I understand what it meant when one uses 'solve' as above, I would also say that as a mathematician, I prefer 'simplify.' Wouldn't you agree?2011-04-19
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    @mr student: In your comment above, you asked about $(\sqrt{2y} + \sqrt{7x})(\sqrt{2y} - \sqrt{7x})$. Yes - it is also true that $(a+b)(a-b) = a^2 + b^2$.2011-04-19
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    @mixedmath: I see no problem whatsoever with "solving a simplification problem". It's a *very* natural phrase for a native English speaker. A Google Books search finds many examples of such usage.2011-04-19
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    i am so confused. because 7x-2y doesn't equal (2y−−√+7x−−√)(2y−−√−7x−−√)2011-04-19
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    I do not understand the notation in your last comment...2011-04-19