Zad.8 [latex]a)\ (frac{1}{3}x-4)^2-x(frac{1}{2}x-1)^2=(frac{1}{3}x)^2-2cdot frac{1}{3}xcdot 4 + 4^2-\ -x[(frac{1}{2}x)^2-2cdot frac{1}{2}xcdot 1 + 1^2]=frac{1}{9}x^2-frac{8}{3}x+16-x(frac{1}{4}x^2-x+1)=\ =frac{1}{9}x^2-frac{8}{3}x+16-frac{1}{4}x^3+x^2-x=-frac{1}{4}x^3+frac{10}{9}x^2-frac{11}{3}x+16=\ =-frac{1}{4}cdot 6^3+frac{10}{9}cdot 6^2-frac{11}{3} cdot 6+16=-frac{1}{4}cdot 216 + frac{10}{9}cdot 36 - frac{11}{3}cdot 6+\ +16=-54+40-22+16=-20\ \[/latex] [latex]b)\ 0,5x^2(4c^3-5)=2x^2c^3-2,5x^2=2cdot (-2)^2cdot 1^3-2,5cdot (-2)^2=\ =2cdot 4-2,5 cdot 4=8-10=-2\ \ [/latex] [latex]c)\ 8a^3+(b^2+6):c=8a^3+frac{b^2}{c}+frac{6}{c}=8cdot (-1)^3+(frac{(-2)^2}{8}+frac{6}{8})=\ =8cdot (-1)+(frac{4}{8}+frac{6}{8})=-8+frac{10}{8}=-8+frac{5}{4}=-8+1frac{1}{4}=-6frac{3}{4}\ \ d)\ 4x-(5y^2+8z^3)=4cdot (-frac{1}{4})-(5cdot 0,2+8cdot (-1)^3)=\ =-1-(1-8)=-1-(-7)=-1+7=6\ [/latex] [latex]e)\ 3m^3+2[m^2-3(2m-1)]=3m^3+2[m^2-6m+3]=\ =3m^3+2m^2-12m+6=3cdot (frac{1}{3})^3+2cdot (frac{1}{3})^2-12cdot frac{1}{3}+6=\=3cdot frac{1}{27}+2cdot frac{1}{9}-4+6= frac{1}{9}+frac{2}{9}-4+6=frac{3}{9}+2=frac{1}{3}+2=2frac{1}{3}\ \[/latex] [latex]f)\ frac{16z^2-2}{2,1-6,4cdot z^3}+z=frac{16cdot (frac{1}{4})^2-2}{2,1-6,4 cdot (frac{1}{4})^3}-frac{1}{4}=frac{1-2}{2,1-frac{64}{10}cdotfrac{1}{64}}-frac{1}{4}=\ =frac{-1}{2,1-frac{1}{10}}-frac{1}{4}=frac{-1}{2,1-0,1}-frac{1}{4} =-frac{1}{2}-frac{1}{4}=-frac{3}{4} [/latex] Zad.3 [latex]a)\ (3xy-5x^2y)-(10xy-2x^2y)=3xy-5x^2y-10xy+2x^2y=\ =-7xy-3x^2y\ \ b)\ (-12abc-4a^2bc)-(abc+a^2bc)+12=\ =-12abc-4a^2bc-abc-a^2bc+12=12 -13abc-5a^2bc\ \ c)\ (1frac{3}{5}x^3+frac{2}{3}y^2-frac{5}{6})-(2,4x^3+y^2-1frac{1}{6})=\ =frac{8}{5}x^3+frac{2}{3}y^2-frac{5}{6}-frac{12}{5}x^3-y^2+frac{7}{6}=-frac{4}{5}x^3-frac{1}{3}y^2+frac{1}{3}[/latex] [latex]d)\ (0,5x^2y^2-frac{2}{3}ab-1)-(-frac{1}{3}x^2y^2+frac{1}{12}ab-frac{1}{4})=\ =frac{1}{2}x^2y^2-frac{2}{3}ab-1+frac{1}{3}x^2y^2-frac{1}{12}ab+frac{1}{4}=frac{5}{6}x^2y^2-frac{3}{4}ab-frac{3}{4}\ \ e)\ (0,4ab-0,5bc+0,1cd)-(-0,3ab+2,5bc-cd)=\ =0,4ab-0,5bc+0,1cd+0,3ab-2,5bc+cd=\ =-0,7ab-3bc+1,1cd\ \ f)\ (4x^n+2x^m+5)-(x^n+x^m+6)=\ =4x^n+2x^m+5-x^n-x^m-6=3x^n+x^m-1[/latex] Zad.5 [latex]a)\ -3ab(-6a^2-2ab-b^2)-(3ab^3+6a^2b^2)=\ =18a^3b+6a^2b^2+3ab^3-3ab^3-6a^2b^2=18a^3b\ \ b\ 6a(5a^2-8b)-10a(6b+7a^2)-3ab=\ =30a^3-48ab-60ab-70a^3-3ab= -40a^3-111ab\ \ [/latex] [latex]c)\ (8x^3-4x^2y^2)-2(3x^2y^2+4x^3) ] cdot (-2x^2y^2)=\ = [8x^3-4x^2y^2-6x^2y^2-8x^3]cdot (-2x^2y^2)=\ =-10x^2y^2 cdot (-2x^2y^2)=20x^4y^4\ \ d)\ 4c-2(c-3)-3[c-3(4-2c)+8]=\ =4c-2c+6-3[c-12+6c+8]=2c+6-3(7c-4)=\ =2c+6-21c+12=18-19c [/latex]
