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[tex](2\sqrt{2}-1)^2-(2\sqrt{2}-1)(1+\sqrt{2})-(2\sqrt{2}+1)^2=\\\\=(2\sqrt{2}-1)^2-(2\sqrt{2}-1)(2\sqrt{2}+1)-(2\sqrt{2}+1)^2=\\\\=(2\sqrt{2})^2-2\cdot 2\sqrt{2}\cdot 1+1^2-[(2\sqrt{2})^2-1^2]-[(2\sqrt{2})^2+2\cdot 2\sqrt{2}\cdot 1+1^2]=\\\\=2^2\cdot (\sqrt{2})^2-4\sqrt{2}+1-[(2^2\cdot(\sqrt{2})^2-1]-[2^2\cdot(\sqrt{2})^2+4\sqrt{2}+1]=\\\\=4\cdot 2-4\sqrt{2}+1-(4\cdot 2-1)-(4\cdot 2+4\sqrt{2}+1)=\\\\=8-4\sqrt{2}+1-8+1-8-4\sqrt{2}-1=\boxed{-8\sqrt{2}-7}[/tex]
Skorzystano z następujących wzorów skróconego mnożenia:
[tex]1.\ (a-b)^2=a^2-2ab+b^2\\\\2.\ (a+b)^2=a^2+2ab+b^2\\\\3.\ (a-b)(a+b)=a^2-b^2[/tex]
