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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{20}{11})(\frac{-20}{13}-x)& =(\color{red}{q}+\color{orange}{\frac{-20}{11}}).(\color{green}{-x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{20}{13}q+\frac{20}{11}x+\frac{20}{11}.\frac{20}{13}& \text{Uitwerken } \\ & =-qx-\frac{20}{13}q+\frac{20}{11}x+\frac{400}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{11}-p)(\frac{-4}{18}+b)& =(\color{red}{-p}+\color{orange}{\frac{-2}{11}}).(\color{green}{b}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{9}p-\frac{2}{11}b+\frac{2}{11}.\frac{2}{9}& \text{Uitwerken } \\ & =-bp+\frac{2}{9}p-\frac{2}{11}b+\frac{4}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{6}{14})(b-\frac{-16}{14})& =(\color{red}{a}+\color{orange}{\frac{3}{7}}).(\color{green}{b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{7}a+\frac{3}{7}b+\frac{3}{7}.\frac{8}{7}& \text{Uitwerken } \\ & =ab+\frac{8}{7}a+\frac{3}{7}b+\frac{24}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-14}{16})(8+b)& =(\color{red}{a}+\color{orange}{\frac{7}{8}}).(\color{green}{b}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ab+8a+\frac{7}{8}b+\frac{7}{8}.8& \text{Uitwerken } \\ & =ab+8a+\frac{7}{8}b+\frac{56}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+8a+\frac{7}{8}b+7 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{11}-q)(q+\frac{-3}{4})& =(\color{red}{-q}+\color{orange}{\frac{9}{11}}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{9}{11})} . \color{green}{(q)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{3}{4}q+\frac{9}{11}q-\frac{9}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =-q^2+(\frac{3}{4}+\frac{9}{11})q-\frac{27}{44} & \text{Neem samen} \\ &=-q^2+\frac{69}{44}q-\frac{27}{44} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-20}{3}+p)(\frac{18}{13}-p)& =(\color{red}{p}+\color{orange}{\frac{-20}{3}}).(\color{green}{-p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{18}{13}p+\frac{20}{3}p-\frac{20}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =-p^2+(\frac{18}{13}+\frac{20}{3})p-\frac{360}{39} & \text{Neem samen} \\ &=-p^2+\frac{314}{39}p-\frac{360}{39} & \text{Maak de som} \\ &=-p^2+\frac{314}{39}p-\frac{120}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-13}{8})(q+\frac{-20}{12})& =(\color{red}{q}+\color{orange}{\frac{-13}{8}}).(\color{green}{q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{3}q-\frac{13}{8}q+\frac{13}{8}.\frac{5}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{3})+(\frac{-13}{8}))q+\frac{65}{24} & \text{Neem samen} \\ &=q^2-\frac{79}{24}q+\frac{65}{24} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{4}+q)(\frac{11}{5}-p)& =(\color{red}{q}+\color{orange}{\frac{-9}{4}}).(\color{green}{-p}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{5}q+\frac{9}{4}p-\frac{9}{4}.\frac{11}{5}& \text{Uitwerken } \\ & =-pq+\frac{11}{5}q+\frac{9}{4}p-\frac{99}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{17}+q)(\frac{4}{20}-p)& =(\color{red}{q}+\color{orange}{\frac{5}{17}}).(\color{green}{-p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{5}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{5}q-\frac{5}{17}p+\frac{5}{17}.\frac{1}{5}& \text{Uitwerken } \\ & =-pq+\frac{1}{5}q-\frac{5}{17}p+\frac{5}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{1}{5}q-\frac{5}{17}p+\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{4}{20})(x-\frac{13}{13})& =(\color{red}{q}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q-\frac{1}{5}x+\frac{1}{5}.1& \text{Uitwerken } \\ & =qx-1q-\frac{1}{5}x+\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-1}{13})(a+\frac{-13}{20})& =(\color{red}{b}+\color{orange}{\frac{-1}{13}}).(\color{green}{a}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{20}b-\frac{1}{13}a+\frac{1}{13}.\frac{13}{20}& \text{Uitwerken } \\ & =ab-\frac{13}{20}b-\frac{1}{13}a+\frac{13}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{20}b-\frac{1}{13}a+\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-10}{10})(a+\frac{8}{13})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{13}x+1a+1.\frac{8}{13}& \text{Uitwerken } \\ & =ax+\frac{8}{13}x+1a+\frac{8}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-25 18:44:58
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