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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{5}{17})(b-\frac{-2}{14})& =(\color{red}{p}+\color{orange}{\frac{5}{17}}).(\color{green}{b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{7}p+\frac{5}{17}b+\frac{5}{17}.\frac{1}{7}& \text{Uitwerken } \\ & =bp+\frac{1}{7}p+\frac{5}{17}b+\frac{5}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-(-6))(p+\frac{-17}{7})& =(\color{red}{p}+\color{orange}{6}).(\color{green}{p}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{7}p+6p-6.\frac{17}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{7})+6)p-(\frac{-102}{7}) & \text{Neem samen} \\ &=p^2+\frac{25}{7}p-(\frac{-102}{7}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(q+\frac{7}{10})(\frac{1}{7}+x)& =(\color{red}{q}+\color{orange}{\frac{7}{10}}).(\color{green}{x}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{7}q+\frac{7}{10}x+\frac{7}{10}.\frac{1}{7}& \text{Uitwerken } \\ & =qx+\frac{1}{7}q+\frac{7}{10}x+\frac{7}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{7}q+\frac{7}{10}x+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{5}{18}+b)(\frac{-2}{13}-a)& =(\color{red}{b}+\color{orange}{\frac{5}{18}}).(\color{green}{-a}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{5}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{13}b-\frac{5}{18}a-\frac{5}{18}.\frac{2}{13}& \text{Uitwerken } \\ & =-ab-\frac{2}{13}b-\frac{5}{18}a-\frac{10}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{2}{13}b-\frac{5}{18}a-\frac{5}{117} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{11}-p)(\frac{-4}{19}-b)& =(\color{red}{-p}+\color{orange}{\frac{13}{11}}).(\color{green}{-b}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{13}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{19}p-\frac{13}{11}b-\frac{13}{11}.\frac{4}{19}& \text{Uitwerken } \\ & =bp+\frac{4}{19}p-\frac{13}{11}b-\frac{52}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{12}-a)(a-\frac{-11}{9})& =(\color{red}{-a}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{11}{9}a-\frac{1}{6}a-\frac{1}{6}.\frac{11}{9}& \text{Uitwerken } \\ & =-a^2+((\frac{-11}{9})+(\frac{-1}{6}))a-\frac{11}{54} & \text{Neem samen} \\ &=-a^2-\frac{25}{18}a-\frac{11}{54} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{7}{9}+a)(a-\frac{13}{2})& =(\color{red}{a}+\color{orange}{\frac{7}{9}}).(\color{green}{a}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{2}a+\frac{7}{9}a-\frac{7}{9}.\frac{13}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{2})+\frac{7}{9})a-(\frac{-91}{18}) & \text{Neem samen} \\ &=a^2-\frac{103}{18}a-(\frac{-91}{18}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{19}-x)(\frac{-20}{5}-q)& =(\color{red}{-x}+\color{orange}{\frac{-9}{19}}).(\color{green}{-q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx+4x+\frac{9}{19}q+\frac{9}{19}.4& \text{Uitwerken } \\ & =qx+4x+\frac{9}{19}q+\frac{36}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-13}{8})(\frac{-5}{5}+a)& =(\color{red}{q}+\color{orange}{\frac{13}{8}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1q+\frac{13}{8}a-\frac{13}{8}.1& \text{Uitwerken } \\ & =aq-1q+\frac{13}{8}a-\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(14-x)(p-\frac{6}{6})& =(\color{red}{-x}+\color{orange}{14}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(14)} . \color{green}{(p)} + \color{orange}{(14)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -px+1x+14p-14.1& \text{Uitwerken } \\ & =-px+1x+14p-14 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{9}+x)(a-\frac{6}{8})& =(\color{red}{x}+\color{orange}{\frac{11}{9}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{4}x+\frac{11}{9}a-\frac{11}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =ax-\frac{3}{4}x+\frac{11}{9}a-\frac{33}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{4}x+\frac{11}{9}a-\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{9}-p)(\frac{9}{5}-a)& =(\color{red}{-p}+\color{orange}{\frac{-19}{9}}).(\color{green}{-a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{5}p+\frac{19}{9}a-\frac{19}{9}.\frac{9}{5}& \text{Uitwerken } \\ & =ap-\frac{9}{5}p+\frac{19}{9}a-\frac{171}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{5}p+\frac{19}{9}a-\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-05 16:54:27
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