[tex](2\sqrt{ 3 }x -3 \sqrt{2} y)^2 -(2 \sqrt{5} x + 3\sqrt{ 3} y)^2 - (2\sqrt{ 7} x +5\sqrt{ 2} y)(2\sqrt{ 7} x - 5 \sqrt{2} y)=\\\\= 4*3x^2 -12\sqrt{3*2}\ xy +18y^2-(4*5x^2 +12\sqrt{5*3}\ xy +27y^2)-[(2\sqrt{7}x)^2-(5\sqrt{2}y)^2]=\\\\=12x^2-12\sqrt{6}xy+18y^2-20x^2-12\sqrt{15}xy-27y^2-(28x^2-50y^2)=\\\\= 12x^2-12\sqrt{6}xy+18y^2-20x^2-12\sqrt{15}xy-27y^2- 28x^2+50y^2 =\\\\=-36x^2-12\sqrt{6}xy-12\sqrt{15}xy+41y^2=-36x^2-12xy(\sqrt{6}+\sqrt{15} )+41y^2[/tex]
[tex](a-b)^2=a^2-2ab+ b^2\\\\(a-b)^2=a^2+2ab+ b^2\\\\(a+b)(a-b)=a^2-b^2[/tex]
