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x^{2}-2x\sqrt{2}+\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\sqrt{2}\right)^{2}.
x^{2}-2x\sqrt{2}+2
The square of \sqrt{2} is 2.
x^{2}-2x\sqrt{2}+\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\sqrt{2}\right)^{2}.
x^{2}-2x\sqrt{2}+2
The square of \sqrt{2} is 2.