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

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  1. \((\frac{8}{11}-a)(\frac{8}{17}-a)\)
  2. \((\frac{-3}{17}+p)(p+\frac{-3}{18})\)
  3. \((\frac{-5}{8}+b)(b+\frac{-17}{2})\)
  4. \((\frac{-3}{18}+q)(\frac{4}{7}+a)\)
  5. \((b+\frac{3}{18})(p+\frac{-6}{19})\)
  6. \((\frac{-13}{16}-a)(b-\frac{14}{9})\)
  7. \((\frac{-2}{14}+a)(b+\frac{-16}{4})\)
  8. \((\frac{2}{15}+q)(\frac{6}{19}+b)\)
  9. \((x-\frac{17}{4})(\frac{13}{10}-a)\)
  10. \((\frac{-17}{20}-b)(a+\frac{-8}{20})\)
  11. \((x+\frac{18}{19})(\frac{-16}{20}+a)\)
  12. \((\frac{14}{20}-b)(b-\frac{16}{17})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{11}-a)(\frac{8}{17}-a)& =(\color{red}{-a}+\color{orange}{\frac{8}{11}}).(\color{green}{-a}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{8}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{8}{17}a-\frac{8}{11}a+\frac{8}{11}.\frac{8}{17}& \text{Uitwerken } \\ & =a^2+((\frac{-8}{17})+(\frac{-8}{11}))a+\frac{64}{187} & \text{Neem samen} \\ &=a^2-\frac{224}{187}a+\frac{64}{187} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{17}+p)(p+\frac{-3}{18})& =(\color{red}{p}+\color{orange}{\frac{-3}{17}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{6}p-\frac{3}{17}p+\frac{3}{17}.\frac{1}{6}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{6})+(\frac{-3}{17}))p+\frac{3}{102} & \text{Neem samen} \\ &=p^2-\frac{35}{102}p+\frac{3}{102} & \text{Maak de som} \\ &=p^2-\frac{35}{102}p+\frac{1}{34} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{8}+b)(b+\frac{-17}{2})& =(\color{red}{b}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{2}b-\frac{5}{8}b+\frac{5}{8}.\frac{17}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{2})+(\frac{-5}{8}))b+\frac{85}{16} & \text{Neem samen} \\ &=b^2-\frac{73}{8}b+\frac{85}{16} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{18}+q)(\frac{4}{7}+a)& =(\color{red}{q}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{7}q-\frac{1}{6}a-\frac{1}{6}.\frac{4}{7}& \text{Uitwerken } \\ & =aq+\frac{4}{7}q-\frac{1}{6}a-\frac{4}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{4}{7}q-\frac{1}{6}a-\frac{2}{21} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b+\frac{3}{18})(p+\frac{-6}{19})& =(\color{red}{b}+\color{orange}{\frac{1}{6}}).(\color{green}{p}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{19}b+\frac{1}{6}p-\frac{1}{6}.\frac{6}{19}& \text{Uitwerken } \\ & =bp-\frac{6}{19}b+\frac{1}{6}p-\frac{6}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{6}{19}b+\frac{1}{6}p-\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{16}-a)(b-\frac{14}{9})& =(\color{red}{-a}+\color{orange}{\frac{-13}{16}}).(\color{green}{b}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{14}{9}a-\frac{13}{16}b+\frac{13}{16}.\frac{14}{9}& \text{Uitwerken } \\ & =-ab+\frac{14}{9}a-\frac{13}{16}b+\frac{182}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{14}{9}a-\frac{13}{16}b+\frac{91}{72} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{14}+a)(b+\frac{-16}{4})& =(\color{red}{a}+\color{orange}{\frac{-1}{7}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ab-4a-\frac{1}{7}b+\frac{1}{7}.4& \text{Uitwerken } \\ & =ab-4a-\frac{1}{7}b+\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{2}{15}+q)(\frac{6}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{2}{15}}).(\color{green}{b}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{2}{15})} . \color{green}{(b)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{6}{19}q+\frac{2}{15}b+\frac{2}{15}.\frac{6}{19}& \text{Uitwerken } \\ & =bq+\frac{6}{19}q+\frac{2}{15}b+\frac{12}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{6}{19}q+\frac{2}{15}b+\frac{4}{95} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{17}{4})(\frac{13}{10}-a)& =(\color{red}{x}+\color{orange}{\frac{-17}{4}}).(\color{green}{-a}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{10}x+\frac{17}{4}a-\frac{17}{4}.\frac{13}{10}& \text{Uitwerken } \\ & =-ax+\frac{13}{10}x+\frac{17}{4}a-\frac{221}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{20}-b)(a+\frac{-8}{20})& =(\color{red}{-b}+\color{orange}{\frac{-17}{20}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{5}b-\frac{17}{20}a+\frac{17}{20}.\frac{2}{5}& \text{Uitwerken } \\ & =-ab+\frac{2}{5}b-\frac{17}{20}a+\frac{34}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{2}{5}b-\frac{17}{20}a+\frac{17}{50} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{18}{19})(\frac{-16}{20}+a)& =(\color{red}{x}+\color{orange}{\frac{18}{19}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{18}{19})} . \color{green}{(a)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{5}x+\frac{18}{19}a-\frac{18}{19}.\frac{4}{5}& \text{Uitwerken } \\ & =ax-\frac{4}{5}x+\frac{18}{19}a-\frac{72}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{20}-b)(b-\frac{16}{17})& =(\color{red}{-b}+\color{orange}{\frac{7}{10}}).(\color{green}{b}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{16}{17}b+\frac{7}{10}b-\frac{7}{10}.\frac{16}{17}& \text{Uitwerken } \\ & =-b^2+(\frac{16}{17}+\frac{7}{10})b-\frac{112}{170} & \text{Neem samen} \\ &=-b^2+\frac{279}{170}b-\frac{112}{170} & \text{Maak de som} \\ &=-b^2+\frac{279}{170}b-\frac{56}{85} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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