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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{18}-q)(b-\frac{-5}{17})& =(\color{red}{-q}+\color{orange}{\frac{-2}{9}}).(\color{green}{b}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{17}q-\frac{2}{9}b-\frac{2}{9}.\frac{5}{17}& \text{Uitwerken } \\ & =-bq-\frac{5}{17}q-\frac{2}{9}b-\frac{10}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{13}-p)(\frac{-5}{10}-a)& =(\color{red}{-p}+\color{orange}{\frac{19}{13}}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{19}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p-\frac{19}{13}a-\frac{19}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p-\frac{19}{13}a-\frac{19}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{16}{20})(\frac{12}{6}+x)& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qx+2q+\frac{4}{5}x+\frac{4}{5}.2& \text{Uitwerken } \\ & =qx+2q+\frac{4}{5}x+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{16}-a)(q+\frac{-11}{18})& =(\color{red}{-a}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{11}{18}a-\frac{3}{8}q+\frac{3}{8}.\frac{11}{18}& \text{Uitwerken } \\ & =-aq+\frac{11}{18}a-\frac{3}{8}q+\frac{33}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{11}{18}a-\frac{3}{8}q+\frac{11}{48} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{3}{2}-q)(q+\frac{9}{5})& =(\color{red}{-q}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{5}q+\frac{3}{2}q+\frac{3}{2}.\frac{9}{5}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{5})+\frac{3}{2})q+(\frac{-27}{10}) & \text{Neem samen} \\ &=-q^2-\frac{3}{10}q+(\frac{-27}{10}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{15}{5}+p)(x+(-14))& =(\color{red}{p}+\color{orange}{3}).(\color{green}{x}+\color{blue}{(-14)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-14)} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = px-14p+3x-3.14& \text{Uitwerken } \\ & =px-14p+3x-42 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-3}{14})(\frac{6}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{-3}{14}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qx+2x-\frac{3}{14}q-\frac{3}{14}.2& \text{Uitwerken } \\ & =qx+2x-\frac{3}{14}q-\frac{6}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+2x-\frac{3}{14}q-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-5}{11})(a+(-8))& =(\color{red}{q}+\color{orange}{\frac{5}{11}}).(\color{green}{a}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-8)} + \color{orange}{(\frac{5}{11})} . \color{green}{(a)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = aq-8q+\frac{5}{11}a-\frac{5}{11}.8& \text{Uitwerken } \\ & =aq-8q+\frac{5}{11}a-\frac{40}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-19}{2})(\frac{17}{11}-a)& =(\color{red}{p}+\color{orange}{\frac{19}{2}}).(\color{green}{-a}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{19}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{11}p-\frac{19}{2}a+\frac{19}{2}.\frac{17}{11}& \text{Uitwerken } \\ & =-ap+\frac{17}{11}p-\frac{19}{2}a+\frac{323}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{4}{18})(a+\frac{12}{7})& =(\color{red}{a}+\color{orange}{\frac{-2}{9}}).(\color{green}{a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{12}{7}a-\frac{2}{9}a-\frac{2}{9}.\frac{12}{7}& \text{Uitwerken } \\ & =a^2+(\frac{12}{7}+(\frac{-2}{9}))a-(\frac{-24}{63}) & \text{Neem samen} \\ &=a^2+\frac{94}{63}a-(\frac{-24}{63}) & \text{Maak de som} \\ &=a^2+\frac{94}{63}a+\frac{8}{21} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(\frac{-5}{12}+a)(\frac{-19}{9}+p)& =(\color{red}{a}+\color{orange}{\frac{-5}{12}}).(\color{green}{p}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{9}a-\frac{5}{12}p+\frac{5}{12}.\frac{19}{9}& \text{Uitwerken } \\ & =ap-\frac{19}{9}a-\frac{5}{12}p+\frac{95}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{20}{8}-x)(\frac{-15}{20}-b)& =(\color{red}{-x}+\color{orange}{\frac{5}{2}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{4}x-\frac{5}{2}b-\frac{5}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =bx+\frac{3}{4}x-\frac{5}{2}b-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-27 22:04:28
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