zad.10 [latex]a) =2(9+6x+x^2)-2(4-4x+x^2)-3(4-x^2)=\ \=18+12x+2x^2-8+8x-2x^2-12+3x^2=3x^2+20x-2\ \ \ b) =4x^2-9y^2-2(16x^2+24xy+9y^2)+2(9x^2-24xy+16y^2)=\ \=4x^2-9y^2-32x^2-48xy-18y^2+18x^2-48xy+32y^2=-10x^2-96xy+5y^2[/latex] Zad.11 [latex]a) =2-2sqrt{2}x+x^2-4x^6+1=3-2sqrt{2} cdot sqrt{2}+(sqrt{2})^2-4(sqrt{2})^6=3-4+2-32=-31\ \ \ b) =x^2+4x+4-4+9x^2-3-2sqrt{3}x-x^2=9x^2+4x-2sqrt{3}x-3=\ \=9cdot (sqrt{3})^2+4cdot sqrt{3}-2sqrt{3}cdot sqrt{3}-3=27+4sqrt{3}-6-3=18+4sqrt{3}\ \ \ c) =x^2-6x+9+sqrt{5}(5-4x^2)-1+2x-x^2=-4sqrt{5}x^2-4x+8+5sqrt{5}=\ \=-4sqrt{5}cdot (-sqrt{5})^2-4cdot (-sqrt{5})+8+5sqrt{5}=-20sqrt{5}+4sqrt{5}+8+5sqrt{5}=8-11sqrt{5}\ \ \ [/latex] [latex]\ d) =x^3+2x^2+x-x^2-2x-1+x^3+1-x^3-3x^2-3x-1+25= x^3-2x^2-4x+24=\ \=(2sqrt{3})^3-2cdot (2sqrt{3})^2-4cdot 2sqrt{3}+24=24sqrt{3}-24-8sqrt{3}+24=16sqrt{3}[/latex] Zad.12 [latex]a) frac{3}{sqrt{3}-1}cdot frac{sqrt{3}+1}{sqrt{3}+1} = frac{3(sqrt{3}+1)}{3-1}=frac{3(sqrt{3}+1)}{2}\ \ \ b) frac{4}{sqrt{2}+3} cdot frac{sqrt{2}-3}{sqrt{2}-3}=frac{4(sqrt{2}+3)}{2-9}=-frac{4(sqrt{2}+3)}{7}\ \ \ c) frac{2sqrt{5}}{sqrt{3}+1}cdot frac{sqrt{3}-1}{sqrt{3}-1}=frac{2sqrt{5}(sqrt{3}-1)}{3-1}=sqrt{5}(sqrt{3}-1)\ \ \[/latex] [latex]d) frac{sqrt{2}}{2sqrt{3}-3}cdot frac{2sqrt{3}+3}{2sqrt{3}+3}=frac{2sqrt{6}+3sqrt{2}}{12-3}=frac{2sqrt{6}+3sqrt{2}}{9}\ \ \ [/latex] reszta zadań później
