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

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

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6  
The usual $x^2-2xy+y^2$ still applies. –  J. M. Apr 19 '11 at 17:03
3  
There is nothing to "solve". You have an expression, not an equation. –  Arturo Magidin Apr 19 '11 at 17:52
    
Did you mean to have it equal to $0$? –  fdart17 Apr 19 '11 at 18:41
    
@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. –  Bill Dubuque Apr 19 '11 at 20:08

1 Answer 1

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-2y –  user9792 Apr 19 '11 at 18:48
    
why on the answer it didn't follow the rule a^2 +b^2 - 2ab –  user9792 Apr 19 '11 at 19:44
    
I dont see 2 before sqrt(14xy) –  user9792 Apr 19 '11 at 19:44
    
@mr student You are absolutely right! I have edited it to include the 2. Good catch. –  mixedmath Apr 19 '11 at 20:44
    
@mixedmath: The use of "solve" here is fine - see my comment above. –  Bill Dubuque Apr 19 '11 at 20:45

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