SOLUTION: If x^2+y^2=20 and xy=30, what is the value of (2x+2y)^2? Thank you in advance!

Question 865791: If x^2+y^2=20 and xy=30, what is the value of (2x+2y)^2?
Thank you in advance!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If x^2+y^2=20 and xy=30, what is the value of (2x+2y)^2?

Thank you in advance!

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First factor out 2 and rewrite things a bit to get

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Now expand out to get

So we have these 3 terms: x^2, 2xy, y^2

We have 2 of them so far. The outer terms x^2 and y^2 and they are from the equation x^2+y^2=20

We just need a 2xy term. Well we have xy=30, so let's multiply both sides by 2 to get 2xy=60.

That wraps up what we need. Let's put it all together.

From above, we found that . Replace with (since ) to get

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Now group up the x^2 and y^2 terms

And replace with 20 (because we're given x^2+y^2=20)

Then replace 2xy with 60 (since we just found that 2xy=60)

Now compute to finish up

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