Final answer to the problem
$4\left(\sqrt{x}+2\sqrt{y}\right)\left(\sqrt{x}-2\sqrt{y}\right)$
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Step-by-step Solution
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1
Factor the polynomial $\left(2\sqrt{x}+4\sqrt{y}\right)$ by it's greatest common factor (GCF): $2$
$2\left(\sqrt{x}+2\sqrt{y}\right)\left(2\sqrt{x}-4\sqrt{y}\right)$
2
Factor the polynomial $\left(2\sqrt{x}-4\sqrt{y}\right)$ by it's greatest common factor (GCF): $2$
$4\left(\sqrt{x}+2\sqrt{y}\right)\left(\sqrt{x}-2\sqrt{y}\right)$
Final answer to the problem
$4\left(\sqrt{x}+2\sqrt{y}\right)\left(\sqrt{x}-2\sqrt{y}\right)$