Zad.1
[tex]4. (2\sqrt2x-\sqrt3y)(2\sqrt2x+\sqrt3y)-(2\sqrt2x-\sqrt3y)(2\sqrt2x-\sqrt3y)=\\=8x^2-3y^2-(8x^2-4\sqrt6xy+3y^2)=8x^2-3y^2-8x^2+4\sqrt6xy-3y^2=4\sqrt6xy-6y^2\\[/tex]
[tex]5.(1\frac23a+2\frac12b)(1\frac23a+2\frac12b)-2\frac{2}{5}(a^2+3ab-5b^2)=\\=(\frac53a+\frac52b)(\frac53a+\frac52b)-2\frac{2}{5}a^2-6\frac{6}{5}ab+10\frac{10}{5}b^2=\\=\frac{25}{9}a^2+\frac{25}{6}ab+\frac{25}{6}ab+\frac{25}{4}b^2-2\frac{2}{5}a^2-7\frac{1}{5}ab+12b^2=\\=2\frac{7}{9}a^2+4\frac{1}{6}ab+4\frac{1}{6}ab+6\frac{1}{4}b^2-2\frac{2}{5}a^2-7\frac{1}{5}ab+12b^2=\\=2\frac{35}{45}a^2-2\frac{18}{45}a^2+8\frac{2}{6}ab-7\frac{1}{5}ab+6\frac{1}{4}b^2+12b^2=[/tex]
[tex]=\frac{17}{45}a^2+8\frac{10}{30}ab-7\frac{6}{30}ab+18\frac{1}{4}b^2=\frac{17}{45}a^2+1\frac{4}{30}ab+18\frac{1}{4}b^2=\frac{17}{45}a^2+1\frac{2}{15}ab+18\frac{1}{4}b^2[/tex]
[tex]6.(7,5x-3,4xy)(-2x+5y)-2,8(5x^2-10xy)=\\=-15x^2+37,5xy+6,8x^2y-17xy^2-9x^2+28xy=\\=6,8x^2y-24x^2+65,5xy-17xy^2[/tex]
[tex]7.(\sqrt6ab-\sqrt2a)(2\sqrt2a+\sqrt6ab)-2\sqrt3a(3ab-2\sqrt{12})=\\=2\sqrt{12}a^2b+6a^2b^2-4a^2-\sqrt{12}ab-6\sqrt3a^2b+4\sqrt{36}a=\\=4\sqrt{3}a^2b+6a^2b^2-4a^2-2\sqrt{3}ab-6\sqrt3a^2b+24a=\\6a^2b^2-2\sqrt3a^2b-4a^2-2\sqrt3ab+24a[/tex]
Zad.2
[tex]\sqrt3(3\sqrt2x-\sqrt3x^2)-(2\sqrt6x+4x^2)=3\sqrt6x-3x^2-2\sqrt6x-4x^2=\sqrt6x-7x^2[/tex]
[tex]-(-2\sqrt6x+8)-(2\sqrt3x-\sqrt2)(2\sqrt3x+\sqrt2)=\\=2\sqrt6x-8-(12x^2-2)=2\sqrt6x-8-12x^2+2=-12x^2+2\sqrt6x-6[/tex]
[tex](2\sqrt2x-\sqrt3)(2\sqrt2x+\sqrt3)-(5x^2+\sqrt6x+1)=8x^2-3-5x^2-\sqrt6x-1=\\=3x^2-\sqrt6x-4[/tex]
[tex]\sqrt3x(2\sqrt3x-4\sqrt8)-(\sqrt6x+2x^2)=6x^2-4\sqrt{24}-\sqrt6x-2x^2=\\=6x^2-4\sqrt{24}x-\sqrt6x-2x^2=4x^2-4*2\sqrt6x-\sqrt6x=4x^2-9\sqrt6x[/tex]
[tex](\sqrt3x-\sqrt2)(\sqrt3x-\sqrt2)=3x^2-2\sqrt6x+2[/tex]
Zad.3
[tex](2x+1)(2x-1)=4x^2-1\\(4x^2-1)-1=4x^2-1-1=4x^2-2[/tex]
Odp. B
