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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-11}{18}-p)(\frac{16}{16}+a)& =(\color{red}{-p}+\color{orange}{\frac{-11}{18}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1p-\frac{11}{18}a-\frac{11}{18}.1& \text{Uitwerken } \\ & =-ap-1p-\frac{11}{18}a-\frac{11}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-5}{18}+a)(\frac{-14}{10}-q)& =(\color{red}{a}+\color{orange}{\frac{-5}{18}}).(\color{green}{-q}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{5}a+\frac{5}{18}q+\frac{5}{18}.\frac{7}{5}& \text{Uitwerken } \\ & =-aq-\frac{7}{5}a+\frac{5}{18}q+\frac{35}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{7}{5}a+\frac{5}{18}q+\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-12}{14})(\frac{-9}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{6}{7}}).(\color{green}{-x}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{6}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{16}p-\frac{6}{7}x-\frac{6}{7}.\frac{9}{16}& \text{Uitwerken } \\ & =-px-\frac{9}{16}p-\frac{6}{7}x-\frac{54}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{9}{16}p-\frac{6}{7}x-\frac{27}{56} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-19}{10}-p)(\frac{-7}{10}-x)& =(\color{red}{-p}+\color{orange}{\frac{-19}{10}}).(\color{green}{-x}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{10}p+\frac{19}{10}x+\frac{19}{10}.\frac{7}{10}& \text{Uitwerken } \\ & =px+\frac{7}{10}p+\frac{19}{10}x+\frac{133}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{5}{11})(a-\frac{4}{20})& =(\color{red}{q}+\color{orange}{\frac{5}{11}}).(\color{green}{a}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{5}{11})} . \color{green}{(a)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{5}q+\frac{5}{11}a-\frac{5}{11}.\frac{1}{5}& \text{Uitwerken } \\ & =aq-\frac{1}{5}q+\frac{5}{11}a-\frac{5}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{5}q+\frac{5}{11}a-\frac{1}{11} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{8}{17})(b+\frac{-6}{20})& =(\color{red}{b}+\color{orange}{\frac{8}{17}}).(\color{green}{b}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{8}{17})} . \color{green}{(b)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{10}b+\frac{8}{17}b-\frac{8}{17}.\frac{3}{10}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{10})+\frac{8}{17})b-(\frac{-24}{170}) & \text{Neem samen} \\ &=b^2+\frac{29}{170}b-(\frac{-24}{170}) & \text{Maak de som} \\ &=b^2+\frac{29}{170}b+\frac{12}{85} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{9}-a)(\frac{-3}{11}-a)& =(\color{red}{-a}+\color{orange}{\frac{11}{9}}).(\color{green}{-a}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{11}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{11}a-\frac{11}{9}a-\frac{11}{9}.\frac{3}{11}& \text{Uitwerken } \\ & =a^2+(\frac{3}{11}+(\frac{-11}{9}))a-(\frac{-33}{99}) & \text{Neem samen} \\ &=a^2-\frac{94}{99}a-(\frac{-33}{99}) & \text{Maak de som} \\ &=a^2-\frac{94}{99}a+\frac{1}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(a-\frac{1}{10})(\frac{16}{8}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aa+2a-\frac{1}{10}a-\frac{1}{10}.2& \text{Uitwerken } \\ & =a^2+(2+(\frac{-1}{10}))a-(\frac{-2}{10}) & \text{Neem samen} \\ &=a^2+\frac{19}{10}a-(\frac{-2}{10}) & \text{Maak de som} \\ &=a^2+\frac{19}{10}a+\frac{1}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(a-\frac{2}{17})(a-\frac{-7}{17})& =(\color{red}{a}+\color{orange}{\frac{-2}{17}}).(\color{green}{a}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{17}a-\frac{2}{17}a-\frac{2}{17}.\frac{7}{17}& \text{Uitwerken } \\ & =a^2+(\frac{7}{17}+(\frac{-2}{17}))a-(\frac{-14}{289}) & \text{Neem samen} \\ &=a^2+\frac{5}{17}a-(\frac{-14}{289}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-11}{11})(\frac{-12}{10}-q)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{6}{5}q-1q-1.\frac{6}{5}& \text{Uitwerken } \\ & =-q^2+((\frac{-6}{5})+(-1))q-\frac{6}{5} & \text{Neem samen} \\ &=-q^2-\frac{11}{5}q-\frac{6}{5} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{5}-p)(\frac{7}{11}-x)& =(\color{red}{-p}+\color{orange}{4}).(\color{green}{-x}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(4)} . \color{green}{(-x)} + \color{orange}{(4)} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{11}p-4x+4.\frac{7}{11}& \text{Uitwerken } \\ & =px-\frac{7}{11}p-4x+\frac{28}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-8}{15})(x+\frac{-11}{8})& =(\color{red}{b}+\color{orange}{\frac{8}{15}}).(\color{green}{x}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{8}b+\frac{8}{15}x-\frac{8}{15}.\frac{11}{8}& \text{Uitwerken } \\ & =bx-\frac{11}{8}b+\frac{8}{15}x-\frac{88}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{11}{8}b+\frac{8}{15}x-\frac{11}{15} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-16 17:06:16
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