\(\left(\sqrt{32}-\sqrt{50}+\sqrt{27}\right).\left(\sqrt{27}+\sqrt{50}\sqrt{32}\right)\)
\(=\left(\sqrt{4^2.2}-\sqrt{5^2.2}+\sqrt{3^2.3}\right).\left(\sqrt{3^2.3}+\sqrt{5^2.2}-\sqrt{4^2.2}\right)\)
\(=\left(4\sqrt{2}-5\sqrt{2}+3\sqrt{3}\right).\left(3\sqrt{3}+5\sqrt{2}-4\sqrt{2}\right)\)
\(=\left(3\sqrt{3}-\sqrt{2}\right).\left(3\sqrt{3}+\sqrt{2}\right)\)
\(=\left(3\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2=27-2\)
\(=25\)
\(\left(\sqrt{32}-\sqrt{50}+\sqrt{27}\right)\left(\sqrt{27}+\sqrt{50}-\sqrt{32}\right)\)
\(=\left(\sqrt{16.2}-\sqrt{25.2}+\sqrt{9.3}\right)\left(\sqrt{9.3}+\sqrt{25.2}-\sqrt{16.2}\right)\)
\(=\left(\sqrt{16}.\sqrt{2}-\sqrt{25}.\sqrt{2}+\sqrt{9}.\sqrt{3}\right)\left(\sqrt{9}.\sqrt{3}+\sqrt{25}.\sqrt{2}-\sqrt{16}.\sqrt{2}\right)\)
\(=\left(4\sqrt{2}-5\sqrt{2}+3\sqrt{3}\right)\left(3\sqrt{3}+5\sqrt{2}-4\sqrt{2}\right)\)
\(=\left(3\sqrt{3}-\sqrt{2}\right)\left(3\sqrt{3}+\sqrt{2}\right)\)
\(=\left(3\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\)
\(=27-2=25\)
