Distributiviteit \((a+r)(b+s)\)

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  1. \((q+\frac{18}{5})(b-\frac{-14}{12})\)
  2. \((\frac{11}{16}-a)(a+\frac{5}{6})\)
  3. \((b+\frac{16}{9})(\frac{-16}{4}-a)\)
  4. \((\frac{-6}{16}+x)(\frac{14}{15}-b)\)
  5. \((\frac{6}{11}+b)(x-\frac{-14}{11})\)
  6. \((p-\frac{-5}{16})(p-\frac{17}{20})\)
  7. \((\frac{2}{5}-q)(\frac{3}{7}-q)\)
  8. \((x+\frac{-9}{14})(\frac{17}{13}-q)\)
  9. \((\frac{-2}{13}-b)(q-\frac{-13}{17})\)
  10. \((\frac{6}{8}+b)(\frac{5}{2}-b)\)
  11. \((x-\frac{18}{15})(x+\frac{2}{11})\)
  12. \((p-\frac{-6}{7})(p+\frac{6}{3})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{18}{5})(b-\frac{-14}{12})& =(\color{red}{q}+\color{orange}{\frac{18}{5}}).(\color{green}{b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{18}{5})} . \color{green}{(b)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{6}q+\frac{18}{5}b+\frac{18}{5}.\frac{7}{6}& \text{Uitwerken } \\ & =bq+\frac{7}{6}q+\frac{18}{5}b+\frac{126}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{6}q+\frac{18}{5}b+\frac{21}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{16}-a)(a+\frac{5}{6})& =(\color{red}{-a}+\color{orange}{\frac{11}{16}}).(\color{green}{a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{11}{16})} . \color{green}{(a)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{6}a+\frac{11}{16}a+\frac{11}{16}.\frac{5}{6}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{6})+\frac{11}{16})a+(\frac{-55}{96}) & \text{Neem samen} \\ &=-a^2-\frac{7}{48}a+(\frac{-55}{96}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b+\frac{16}{9})(\frac{-16}{4}-a)& =(\color{red}{b}+\color{orange}{\frac{16}{9}}).(\color{green}{-a}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(\frac{16}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ab-4b-\frac{16}{9}a-\frac{16}{9}.4& \text{Uitwerken } \\ & =-ab-4b-\frac{16}{9}a-\frac{64}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{16}+x)(\frac{14}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{-b}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{14}{15}x+\frac{3}{8}b-\frac{3}{8}.\frac{14}{15}& \text{Uitwerken } \\ & =-bx+\frac{14}{15}x+\frac{3}{8}b-\frac{42}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{14}{15}x+\frac{3}{8}b-\frac{7}{20} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{11}+b)(x-\frac{-14}{11})& =(\color{red}{b}+\color{orange}{\frac{6}{11}}).(\color{green}{x}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{6}{11})} . \color{green}{(x)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{14}{11}b+\frac{6}{11}x+\frac{6}{11}.\frac{14}{11}& \text{Uitwerken } \\ & =bx+\frac{14}{11}b+\frac{6}{11}x+\frac{84}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-5}{16})(p-\frac{17}{20})& =(\color{red}{p}+\color{orange}{\frac{5}{16}}).(\color{green}{p}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{5}{16})} . \color{green}{(p)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{20}p+\frac{5}{16}p-\frac{5}{16}.\frac{17}{20}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{20})+\frac{5}{16})p-(\frac{-85}{320}) & \text{Neem samen} \\ &=p^2-\frac{43}{80}p-(\frac{-85}{320}) & \text{Maak de som} \\ &=p^2-\frac{43}{80}p+\frac{17}{64} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{2}{5}-q)(\frac{3}{7}-q)& =(\color{red}{-q}+\color{orange}{\frac{2}{5}}).(\color{green}{-q}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{7}q-\frac{2}{5}q+\frac{2}{5}.\frac{3}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{7})+(\frac{-2}{5}))q+\frac{6}{35} & \text{Neem samen} \\ &=q^2-\frac{29}{35}q+\frac{6}{35} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-9}{14})(\frac{17}{13}-q)& =(\color{red}{x}+\color{orange}{\frac{-9}{14}}).(\color{green}{-q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{13}x+\frac{9}{14}q-\frac{9}{14}.\frac{17}{13}& \text{Uitwerken } \\ & =-qx+\frac{17}{13}x+\frac{9}{14}q-\frac{153}{182} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-2}{13}-b)(q-\frac{-13}{17})& =(\color{red}{-b}+\color{orange}{\frac{-2}{13}}).(\color{green}{q}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{17}b-\frac{2}{13}q-\frac{2}{13}.\frac{13}{17}& \text{Uitwerken } \\ & =-bq-\frac{13}{17}b-\frac{2}{13}q-\frac{26}{221} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{13}{17}b-\frac{2}{13}q-\frac{2}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{6}{8}+b)(\frac{5}{2}-b)& =(\color{red}{b}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{5}{2}b-\frac{3}{4}b+\frac{3}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{5}{2}+(\frac{-3}{4}))b+(\frac{-15}{8}) & \text{Neem samen} \\ &=-b^2+\frac{7}{4}b+(\frac{-15}{8}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x-\frac{18}{15})(x+\frac{2}{11})& =(\color{red}{x}+\color{orange}{\frac{-6}{5}}).(\color{green}{x}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{11}x-\frac{6}{5}x-\frac{6}{5}.\frac{2}{11}& \text{Uitwerken } \\ & =x^2+(\frac{2}{11}+(\frac{-6}{5}))x-(\frac{-12}{55}) & \text{Neem samen} \\ &=x^2-\frac{56}{55}x-(\frac{-12}{55}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-6}{7})(p+\frac{6}{3})& =(\color{red}{p}+\color{orange}{\frac{6}{7}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pp+2p+\frac{6}{7}p+\frac{6}{7}.2& \text{Uitwerken } \\ & =p^2+(2+\frac{6}{7})p+\frac{12}{7} & \text{Neem samen} \\ &=p^2+\frac{20}{7}p+\frac{12}{7} & \text{Maak de som} \\\end{align}\)
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