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

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. – J. M. Apr 19 '11 at 17:03
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

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