Sprawdzamy, czy równość jest prawdziwa dla którejś z podanych liczb.

$\text{A.}$  

$L={\left(-\sqrt{2}\cdot \sqrt{2}-2\right)}^2={\left(-2-2\right)}^2={\left(-4\right)}^2=16$  

$P={\left(2+\sqrt{2}\right)}^2=4+4\sqrt{2}+2=6+4\sqrt{2}$  

$L\ne P$  

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$\text{B.}$  

$L={\left(\sqrt{2}\cdot \sqrt{2}-2\right)}^2={\left(2-2\right)}^2=0^2=0$  

$P={\left(2+\sqrt{2}\right)}^2=4+4\sqrt{2}+2=6+4\sqrt{2}$  

$L\ne P$  

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$\text{C.}$  

$L={\left(-1\cdot \sqrt{2}-2\right)}^2={\left(-\sqrt{2}-2\right)}^2=2+4\sqrt{2}+4=6+4\sqrt{2}$  

$P={\left(2+\sqrt{2}\right)}^2=4+4\sqrt{2}+2=6+4\sqrt{2}$  

$L=P$  

Odpowiedź: C