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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-10}{18})(\frac{-6}{6}-b)& =(\color{red}{q}+\color{orange}{\frac{5}{9}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bq-1q-\frac{5}{9}b-\frac{5}{9}.1& \text{Uitwerken } \\ & =-bq-1q-\frac{5}{9}b-\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{1}{13})(\frac{15}{4}+b)& =(\color{red}{q}+\color{orange}{\frac{1}{13}}).(\color{green}{b}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{4}q+\frac{1}{13}b+\frac{1}{13}.\frac{15}{4}& \text{Uitwerken } \\ & =bq+\frac{15}{4}q+\frac{1}{13}b+\frac{15}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{8}+a)(q+\frac{-5}{15})& =(\color{red}{a}+\color{orange}{\frac{-9}{4}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{3}a-\frac{9}{4}q+\frac{9}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =aq-\frac{1}{3}a-\frac{9}{4}q+\frac{9}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{3}a-\frac{9}{4}q+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{3}+a)(p+\frac{-3}{11})& =(\color{red}{a}+\color{orange}{\frac{11}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{11}{3})} . \color{green}{(p)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{11}a+\frac{11}{3}p-\frac{11}{3}.\frac{3}{11}& \text{Uitwerken } \\ & =ap-\frac{3}{11}a+\frac{11}{3}p-\frac{33}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{11}a+\frac{11}{3}p-1 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{19}{8})(\frac{9}{20}-p)& =(\color{red}{a}+\color{orange}{\frac{19}{8}}).(\color{green}{-p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{19}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{20}a-\frac{19}{8}p+\frac{19}{8}.\frac{9}{20}& \text{Uitwerken } \\ & =-ap+\frac{9}{20}a-\frac{19}{8}p+\frac{171}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{11}-p)(\frac{-10}{4}+b)& =(\color{red}{-p}+\color{orange}{\frac{3}{11}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{3}{11})} . \color{green}{(b)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{2}p+\frac{3}{11}b-\frac{3}{11}.\frac{5}{2}& \text{Uitwerken } \\ & =-bp+\frac{5}{2}p+\frac{3}{11}b-\frac{15}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{19}{4})(\frac{14}{17}+x)& =(\color{red}{p}+\color{orange}{\frac{19}{4}}).(\color{green}{x}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{19}{4})} . \color{green}{(x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{17}p+\frac{19}{4}x+\frac{19}{4}.\frac{14}{17}& \text{Uitwerken } \\ & =px+\frac{14}{17}p+\frac{19}{4}x+\frac{266}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{14}{17}p+\frac{19}{4}x+\frac{133}{34} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{7}-q)(a-\frac{14}{4})& =(\color{red}{-q}+\color{orange}{\frac{15}{7}}).(\color{green}{a}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{15}{7})} . \color{green}{(a)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{2}q+\frac{15}{7}a-\frac{15}{7}.\frac{7}{2}& \text{Uitwerken } \\ & =-aq+\frac{7}{2}q+\frac{15}{7}a-\frac{105}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{7}{2}q+\frac{15}{7}a-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{7}+q)(q-\frac{-1}{20})& =(\color{red}{q}+\color{orange}{\frac{3}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{20}q+\frac{3}{7}q+\frac{3}{7}.\frac{1}{20}& \text{Uitwerken } \\ & =q^2+(\frac{1}{20}+\frac{3}{7})q+\frac{3}{140} & \text{Neem samen} \\ &=q^2+\frac{67}{140}q+\frac{3}{140} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(x+\frac{9}{17})(\frac{14}{12}-p)& =(\color{red}{x}+\color{orange}{\frac{9}{17}}).(\color{green}{-p}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{9}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{6}x-\frac{9}{17}p+\frac{9}{17}.\frac{7}{6}& \text{Uitwerken } \\ & =-px+\frac{7}{6}x-\frac{9}{17}p+\frac{63}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{7}{6}x-\frac{9}{17}p+\frac{21}{34} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{19}{19}-a)(\frac{-16}{9}-p)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{9}a-1p-1.\frac{16}{9}& \text{Uitwerken } \\ & =ap+\frac{16}{9}a-1p-\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{8}{5})(q-5)& =(\color{red}{x}+\color{orange}{\frac{8}{5}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(\frac{8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = qx-5x+\frac{8}{5}q-\frac{8}{5}.5& \text{Uitwerken } \\ & =qx-5x+\frac{8}{5}q-\frac{40}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-5x+\frac{8}{5}q-8 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-29 05:23:06
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