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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{13}{12})(p-\frac{-9}{13})& =(\color{red}{p}+\color{orange}{\frac{13}{12}}).(\color{green}{p}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{13}{12})} . \color{green}{(p)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{13}p+\frac{13}{12}p+\frac{13}{12}.\frac{9}{13}& \text{Uitwerken } \\ & =p^2+(\frac{9}{13}+\frac{13}{12})p+\frac{117}{156} & \text{Neem samen} \\ &=p^2+\frac{277}{156}p+\frac{117}{156} & \text{Maak de som} \\ &=p^2+\frac{277}{156}p+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{1}{7}+b)(\frac{-16}{14}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{7}}).(\color{green}{q}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{7}b+\frac{1}{7}q-\frac{1}{7}.\frac{8}{7}& \text{Uitwerken } \\ & =bq-\frac{8}{7}b+\frac{1}{7}q-\frac{8}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-7}{7})(x+\frac{2}{18})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{9}p-1x-1.\frac{1}{9}& \text{Uitwerken } \\ & =px+\frac{1}{9}p-1x-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{2}+q)(x-\frac{11}{7})& =(\color{red}{q}+\color{orange}{\frac{-9}{2}}).(\color{green}{x}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{7}q-\frac{9}{2}x+\frac{9}{2}.\frac{11}{7}& \text{Uitwerken } \\ & =qx-\frac{11}{7}q-\frac{9}{2}x+\frac{99}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-18}{11})(a+\frac{2}{6})& =(\color{red}{a}+\color{orange}{\frac{18}{11}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{18}{11})} . \color{green}{(a)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{3}a+\frac{18}{11}a+\frac{18}{11}.\frac{1}{3}& \text{Uitwerken } \\ & =a^2+(\frac{1}{3}+\frac{18}{11})a+\frac{18}{33} & \text{Neem samen} \\ &=a^2+\frac{65}{33}a+\frac{18}{33} & \text{Maak de som} \\ &=a^2+\frac{65}{33}a+\frac{6}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-8}{7})(\frac{-3}{2}+x)& =(\color{red}{x}+\color{orange}{\frac{8}{7}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{2}x+\frac{8}{7}x-\frac{8}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{2})+\frac{8}{7})x-(\frac{-24}{14}) & \text{Neem samen} \\ &=x^2-\frac{5}{14}x-(\frac{-24}{14}) & \text{Maak de som} \\ &=x^2-\frac{5}{14}x+\frac{12}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{7}-b)(b-\frac{3}{19})& =(\color{red}{-b}+\color{orange}{\frac{-17}{7}}).(\color{green}{b}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{3}{19}b-\frac{17}{7}b+\frac{17}{7}.\frac{3}{19}& \text{Uitwerken } \\ & =-b^2+(\frac{3}{19}+(\frac{-17}{7}))b+(\frac{-51}{133}) & \text{Neem samen} \\ &=-b^2-\frac{302}{133}b+(\frac{-51}{133}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{5}+q)(\frac{-19}{4}+q)& =(\color{red}{q}+\color{orange}{\frac{17}{5}}).(\color{green}{q}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{17}{5})} . \color{green}{(q)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{4}q+\frac{17}{5}q-\frac{17}{5}.\frac{19}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{4})+\frac{17}{5})q-(\frac{-323}{20}) & \text{Neem samen} \\ &=q^2-\frac{27}{20}q-(\frac{-323}{20}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{16}-b)(p-\frac{-7}{12})& =(\color{red}{-b}+\color{orange}{\frac{-5}{4}}).(\color{green}{p}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{12}b-\frac{5}{4}p-\frac{5}{4}.\frac{7}{12}& \text{Uitwerken } \\ & =-bp-\frac{7}{12}b-\frac{5}{4}p-\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-8}{8})(q-\frac{10}{10})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a+1q-1.1& \text{Uitwerken } \\ & =aq-1a+1q-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{5}+b)(a+\frac{5}{18})& =(\color{red}{b}+\color{orange}{\frac{11}{5}}).(\color{green}{a}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{11}{5})} . \color{green}{(a)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{18}b+\frac{11}{5}a+\frac{11}{5}.\frac{5}{18}& \text{Uitwerken } \\ & =ab+\frac{5}{18}b+\frac{11}{5}a+\frac{55}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{18}b+\frac{11}{5}a+\frac{11}{18} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{19}{16})(\frac{-11}{2}-p)& =(\color{red}{a}+\color{orange}{\frac{19}{16}}).(\color{green}{-p}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{19}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{2}a-\frac{19}{16}p-\frac{19}{16}.\frac{11}{2}& \text{Uitwerken } \\ & =-ap-\frac{11}{2}a-\frac{19}{16}p-\frac{209}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-01 22:23:50
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