1.
a)
[tex](\sqrt3+\sqrt8)^2=(\sqrt3)^2+2*\sqrt3*\sqrt8+(\sqrt8)^2=3+2\sqrt{24}+8=11+2\sqrt{4*6}=11+4\sqrt6[/tex]
b)
[tex](\sqrt3+2\sqrt6)^2=(\sqrt3)^2+2*\sqrt3*2\sqrt6+(2\sqrt6)^2=3+4\sqrt{18}+4*6=3+4\sqrt{9*2}+24=27+12\sqrt2[/tex]
c)
[tex](10-\sqrt3)(10+\sqrt3)=10^2-(\sqrt3)^2=100-3=97[/tex]
2.
a)
[tex](5+\sqrt3x)^2=5^2+2*5*\sqrt3x+(\sqrt3x)^2=25+10\sqrt3x+3x^2[/tex]
b)
[tex](\frac16x-2)^2=(\frac16x)^2-2*\frac16x*2+2^2=\frac{x^2}{36}-\frac{4x}6+4=\frac{x^2}{36}-\frac{2x}3+4[/tex]
c)
[tex](0,2x+\sqrt7)(0,2x-\sqrt7)=(0,2x)^2-(\sqrt7)^2=0,04x^2-7[/tex]
3.
[tex](\sqrt2x+5)^2>2x^2+5\\2x^2+10\sqrt2x+25>2x^2+5\\2x^2+10\sqrt2x-2x^2>5-25\\10\sqrt2x>-20 /:10\\\sqrt2x>-2 /:(\sqrt2)\\x>-\frac{2}{\sqrt2}\\x>-\frac{2\sqrt2}2\\x>-\sqrt2\\[/tex]
4.
a)
[tex](x-4)(x+4)-(2x+1)^2+(x-5)^2=\\x^2-4^2-((2x)^2+2*2x*1+1^2)+(x^2-2*x*5+5^2)=\\x^2-16-(4x^2+4x+1)+(x^2-10x+25)=\\x^2-16-4x^2-4x-1+x^2-10x+25=\\-2x^2-14x+8[/tex]
b)
[tex]-(-5x-2)^2-(-6x-3)^2=\\-((-5x)^2-2*(-5x)*2+2^2)-((-6x)^2-2*(-6x)*3+3^2)=\\-(25x^2+20x+4)-(36x^2+36x+9)=\\-25x^2-20x-4-36x^2-36x-9=\\-61x^2-56x-13[/tex]
