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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{13}+a)(a+\frac{2}{14})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{7}a-1a-1.\frac{1}{7}& \text{Uitwerken } \\ & =a^2+(\frac{1}{7}+(-1))a-(\frac{-1}{7}) & \text{Neem samen} \\ &=a^2-\frac{6}{7}a-(\frac{-1}{7}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{19}-a)(a-\frac{-9}{10})& =(\color{red}{-a}+\color{orange}{\frac{-17}{19}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{9}{10}a-\frac{17}{19}a-\frac{17}{19}.\frac{9}{10}& \text{Uitwerken } \\ & =-a^2+((\frac{-9}{10})+(\frac{-17}{19}))a-\frac{153}{190} & \text{Neem samen} \\ &=-a^2-\frac{341}{190}a-\frac{153}{190} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(q-\frac{13}{10})(x-\frac{16}{11})& =(\color{red}{q}+\color{orange}{\frac{-13}{10}}).(\color{green}{x}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{11}q-\frac{13}{10}x+\frac{13}{10}.\frac{16}{11}& \text{Uitwerken } \\ & =qx-\frac{16}{11}q-\frac{13}{10}x+\frac{208}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{16}{11}q-\frac{13}{10}x+\frac{104}{55} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{11}-q)(x-\frac{-11}{10})& =(\color{red}{-q}+\color{orange}{\frac{15}{11}}).(\color{green}{x}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{15}{11})} . \color{green}{(x)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{10}q+\frac{15}{11}x+\frac{15}{11}.\frac{11}{10}& \text{Uitwerken } \\ & =-qx-\frac{11}{10}q+\frac{15}{11}x+\frac{165}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{11}{10}q+\frac{15}{11}x+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{19}{10}+p)(x+\frac{-16}{14})& =(\color{red}{p}+\color{orange}{\frac{19}{10}}).(\color{green}{x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{19}{10})} . \color{green}{(x)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{8}{7}p+\frac{19}{10}x-\frac{19}{10}.\frac{8}{7}& \text{Uitwerken } \\ & =px-\frac{8}{7}p+\frac{19}{10}x-\frac{152}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{8}{7}p+\frac{19}{10}x-\frac{76}{35} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(17-x)(a+\frac{-9}{12})& =(\color{red}{-x}+\color{orange}{17}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(17)} . \color{green}{(a)} + \color{orange}{(17)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{4}x+17a-17.\frac{3}{4}& \text{Uitwerken } \\ & =-ax+\frac{3}{4}x+17a-\frac{51}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{9}{18})(\frac{-12}{20}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{5}q+\frac{1}{2}x-\frac{1}{2}.\frac{3}{5}& \text{Uitwerken } \\ & =qx-\frac{3}{5}q+\frac{1}{2}x-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+(-7))(\frac{-8}{12}+a)& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-7)} . \color{green}{(a)} + \color{orange}{(-7)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{3}a-7a+7.\frac{2}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{3})+(-7))a+\frac{14}{3} & \text{Neem samen} \\ &=a^2-\frac{23}{3}a+\frac{14}{3} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{6}+q)(\frac{-12}{11}-b)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{12}{11}q-1b-1.\frac{12}{11}& \text{Uitwerken } \\ & =-bq-\frac{12}{11}q-1b-\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-16}{16})(b+\frac{5}{17})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{17}b-1b-1.\frac{5}{17}& \text{Uitwerken } \\ & =b^2+(\frac{5}{17}+(-1))b-(\frac{-5}{17}) & \text{Neem samen} \\ &=b^2-\frac{12}{17}b-(\frac{-5}{17}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x-\frac{20}{2})(q+\frac{6}{6})& =(\color{red}{x}+\color{orange}{(-10)}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(-10)} . \color{green}{(q)} + \color{orange}{(-10)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1x-10q-10.1& \text{Uitwerken } \\ & =qx+1x-10q-10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-13}{11})(\frac{-18}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{-13}{11}}).(\color{green}{-q}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{10}p+\frac{13}{11}q+\frac{13}{11}.\frac{9}{10}& \text{Uitwerken } \\ & =-pq-\frac{9}{10}p+\frac{13}{11}q+\frac{117}{110} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-02 11:02:19
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