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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-10}{19})(x-\frac{2}{20})& =(\color{red}{p}+\color{orange}{\frac{10}{19}}).(\color{green}{x}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{10}{19})} . \color{green}{(x)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{10}p+\frac{10}{19}x-\frac{10}{19}.\frac{1}{10}& \text{Uitwerken } \\ & =px-\frac{1}{10}p+\frac{10}{19}x-\frac{10}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{1}{10}p+\frac{10}{19}x-\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-20}{14})(b+\frac{5}{5})& =(\color{red}{p}+\color{orange}{\frac{-10}{7}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-\frac{10}{7}b-\frac{10}{7}.1& \text{Uitwerken } \\ & =bp+1p-\frac{10}{7}b-\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{7}+p)(\frac{18}{18}-p)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pp+1p+1p-1.1& \text{Uitwerken } \\ & =-p^2+(1+1)p-1 & \text{Neem samen} \\ &=-p^2+2p-1 & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{17}-p)(\frac{1}{10}-x)& =(\color{red}{-p}+\color{orange}{\frac{15}{17}}).(\color{green}{-x}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{15}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{10}p-\frac{15}{17}x+\frac{15}{17}.\frac{1}{10}& \text{Uitwerken } \\ & =px-\frac{1}{10}p-\frac{15}{17}x+\frac{15}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{1}{10}p-\frac{15}{17}x+\frac{3}{34} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-1}{8})(b+\frac{-18}{12})& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{2}b-\frac{1}{8}b+\frac{1}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{2})+(\frac{-1}{8}))b+\frac{3}{16} & \text{Neem samen} \\ &=b^2-\frac{13}{8}b+\frac{3}{16} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{14}-p)(a+\frac{-12}{8})& =(\color{red}{-p}+\color{orange}{\frac{17}{14}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{2}p+\frac{17}{14}a-\frac{17}{14}.\frac{3}{2}& \text{Uitwerken } \\ & =-ap+\frac{3}{2}p+\frac{17}{14}a-\frac{51}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-3}{5})(\frac{-19}{20}+q)& =(\color{red}{a}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{20}a-\frac{3}{5}q+\frac{3}{5}.\frac{19}{20}& \text{Uitwerken } \\ & =aq-\frac{19}{20}a-\frac{3}{5}q+\frac{57}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{5}{15}-q)(\frac{13}{5}-x)& =(\color{red}{-q}+\color{orange}{\frac{1}{3}}).(\color{green}{-x}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{5}q-\frac{1}{3}x+\frac{1}{3}.\frac{13}{5}& \text{Uitwerken } \\ & =qx-\frac{13}{5}q-\frac{1}{3}x+\frac{13}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{19}+b)(\frac{18}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{-20}{19}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{3}{2}b+\frac{20}{19}b-\frac{20}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{3}{2}+\frac{20}{19})b-\frac{60}{38} & \text{Neem samen} \\ &=-b^2+\frac{97}{38}b-\frac{60}{38} & \text{Maak de som} \\ &=-b^2+\frac{97}{38}b-\frac{30}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(a-\frac{16}{4})(b-\frac{15}{10})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{2}a-4b+4.\frac{3}{2}& \text{Uitwerken } \\ & =ab-\frac{3}{2}a-4b+\frac{12}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{2}a-4b+6 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p+\frac{11}{6})(\frac{-3}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{11}{6}}).(\color{green}{-a}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{11}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{14}p-\frac{11}{6}a-\frac{11}{6}.\frac{3}{14}& \text{Uitwerken } \\ & =-ap-\frac{3}{14}p-\frac{11}{6}a-\frac{33}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{14}p-\frac{11}{6}a-\frac{11}{28} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{6}{6})(a+\frac{-6}{14})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{7}q+1a-1.\frac{3}{7}& \text{Uitwerken } \\ & =aq-\frac{3}{7}q+1a-\frac{3}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-02 05:15:58
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