[tex]1) \\ a^2-4ab+4b^2 = \\
=a^2-4ab+2^2b^2=a^2-2(a\cdot2b)+(2b)^2= \boxed{(a - 2b)^2} \\
a = 1- \sqrt{3} \\
b= 1+ \sqrt{3} \\
\Longrightarrow~~ (a - 2b)^2 = (1- \sqrt{3} -2(1+\sqrt{3})^2 =\\
(1- \sqrt{3} -2-2\sqrt{3})^2 = (-1- 3\sqrt{3})^2 = 1+6\sqrt{3} +27 =\boxed{\boxed{28+6\sqrt{3}}} [/tex]
[tex]2) \\
(x^2 \sqrt{2} -x \sqrt{3}+ \sqrt{5} )\cdot (x^2 \sqrt{2} +x \sqrt{3}+ \sqrt{5} )-(x^2 \sqrt{2} + \sqrt{5})^2 = \\
=[(x^2 \sqrt{2} + \sqrt{5}) -x\sqrt{3} ]\cdot [(x^2 \sqrt{2} + \sqrt{5}) +x\sqrt{3} ]-(x^2 \sqrt{2} + \sqrt{5})^2 = ... \\
\texttt{Pentru primele 2 paranteze patrate aplicam formula:} \\
(a-b)(a+b)= a^2-b^2, ~~unde ~~a = (x^2 \sqrt{2} + \sqrt{5}) ~~si ~~b= x\sqrt{3} [/tex]
[tex]...= \underline{(x^2 \sqrt{2} + \sqrt{5})^2} - (x\sqrt{3} )^2 \underline{- (x^2 \sqrt{2} + \sqrt{5})^2} = - (x\sqrt{3} )^2 = \boxed{\boxed{-3x^2}} [/tex]
