[tex](a+b)^{3} = a^{3}+3a^{2}b + 3ab^{2}+b^{3}\\\\(a-b)(a+b) = a^{2}-b^{2}[/tex]
[tex](26-15\sqrt{3})(2+\sqrt{3})^{3} =\\\\=(26-15\sqrt{3})(2^{3}+3\cdot2^{2}\cdot\sqrt{3}+3\cdot2\cdot\sqrt{3}^{2}+\sqrt{3}^{3})=\\\\=(26-15\sqrt{3})(8+12\sqrt{3}+18+3\sqrt{3})=\\\\=(26-15\sqrt{3})(26+15\sqrt{3})=\\\\=26^{2}-(15\sqrt{3})^{2} = 676-675 = 1 \ \in N\\\\c.n.w.[/tex]
