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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{6}{17})(\frac{-3}{12}+x)& =(\color{red}{q}+\color{orange}{\frac{6}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{6}{17})} . \color{green}{(x)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{4}q+\frac{6}{17}x-\frac{6}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =qx-\frac{1}{4}q+\frac{6}{17}x-\frac{6}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{4}q+\frac{6}{17}x-\frac{3}{34} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-11}{11})(\frac{-4}{15}-x)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{15}b-1x-1.\frac{4}{15}& \text{Uitwerken } \\ & =-bx-\frac{4}{15}b-1x-\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-5}{19})(\frac{-4}{9}+a)& =(\color{red}{b}+\color{orange}{\frac{5}{19}}).(\color{green}{a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{9}b+\frac{5}{19}a-\frac{5}{19}.\frac{4}{9}& \text{Uitwerken } \\ & =ab-\frac{4}{9}b+\frac{5}{19}a-\frac{20}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{2}+a)(b+\frac{-1}{11})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{11}a-1b+1.\frac{1}{11}& \text{Uitwerken } \\ & =ab-\frac{1}{11}a-1b+\frac{1}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{10}-p)(a+\frac{14}{7})& =(\color{red}{-p}+\color{orange}{\frac{-8}{5}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(2)} + \color{orange}{(\frac{-8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap-2p-\frac{8}{5}a-\frac{8}{5}.2& \text{Uitwerken } \\ & =-ap-2p-\frac{8}{5}a-\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-15}{14}+b)(\frac{17}{20}+a)& =(\color{red}{b}+\color{orange}{\frac{-15}{14}}).(\color{green}{a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{20}b-\frac{15}{14}a-\frac{15}{14}.\frac{17}{20}& \text{Uitwerken } \\ & =ab+\frac{17}{20}b-\frac{15}{14}a-\frac{255}{280} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{17}{20}b-\frac{15}{14}a-\frac{51}{56} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{2}+q)(x+\frac{-11}{16})& =(\color{red}{q}+\color{orange}{\frac{11}{2}}).(\color{green}{x}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{11}{2})} . \color{green}{(x)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{16}q+\frac{11}{2}x-\frac{11}{2}.\frac{11}{16}& \text{Uitwerken } \\ & =qx-\frac{11}{16}q+\frac{11}{2}x-\frac{121}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{13}+b)(\frac{3}{12}-x)& =(\color{red}{b}+\color{orange}{\frac{-4}{13}}).(\color{green}{-x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{4}b+\frac{4}{13}x-\frac{4}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =-bx+\frac{1}{4}b+\frac{4}{13}x-\frac{4}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{1}{4}b+\frac{4}{13}x-\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-11}{10}-q)(\frac{-16}{4}+q)& =(\color{red}{-q}+\color{orange}{\frac{-11}{10}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-11}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -qq+4q-\frac{11}{10}q+\frac{11}{10}.4& \text{Uitwerken } \\ & =-q^2+(4+(\frac{-11}{10}))q+(\frac{-44}{10}) & \text{Neem samen} \\ &=-q^2+\frac{29}{10}q+(\frac{-44}{10}) & \text{Maak de som} \\ &=-q^2+\frac{29}{10}q+(\frac{-22}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}((-20)+q)(q-\frac{4}{5})& =(\color{red}{q}+\color{orange}{(-20)}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(-20)} . \color{green}{(q)} + \color{orange}{(-20)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{5}q-20q+20.\frac{4}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{5})+(-20))q+\frac{80}{5} & \text{Neem samen} \\ &=q^2-\frac{104}{5}q+\frac{80}{5} & \text{Maak de som} \\ &=q^2-\frac{104}{5}q+16 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-13}{18})(\frac{16}{18}-b)& =(\color{red}{p}+\color{orange}{\frac{13}{18}}).(\color{green}{-b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{13}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{9}p-\frac{13}{18}b+\frac{13}{18}.\frac{8}{9}& \text{Uitwerken } \\ & =-bp+\frac{8}{9}p-\frac{13}{18}b+\frac{104}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{8}{9}p-\frac{13}{18}b+\frac{52}{81} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{6}{10})(\frac{-8}{19}+x)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{x}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{19}q-\frac{3}{5}x+\frac{3}{5}.\frac{8}{19}& \text{Uitwerken } \\ & =qx-\frac{8}{19}q-\frac{3}{5}x+\frac{24}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-22 16:46:16
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