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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{5}{17})(\frac{-5}{2}-x)& =(\color{red}{a}+\color{orange}{\frac{5}{17}}).(\color{green}{-x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{5}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{2}a-\frac{5}{17}x-\frac{5}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =-ax-\frac{5}{2}a-\frac{5}{17}x-\frac{25}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{3}{3})(p-\frac{19}{13})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{13}x+1p-1.\frac{19}{13}& \text{Uitwerken } \\ & =px-\frac{19}{13}x+1p-\frac{19}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{5}+a)(q+\frac{5}{11})& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{11}a+\frac{6}{5}q+\frac{6}{5}.\frac{5}{11}& \text{Uitwerken } \\ & =aq+\frac{5}{11}a+\frac{6}{5}q+\frac{30}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{11}a+\frac{6}{5}q+\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{17}{20})(\frac{-2}{12}-a)& =(\color{red}{a}+\color{orange}{\frac{-17}{20}}).(\color{green}{-a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{6}a+\frac{17}{20}a+\frac{17}{20}.\frac{1}{6}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{6})+\frac{17}{20})a+(\frac{-17}{120}) & \text{Neem samen} \\ &=-a^2+\frac{41}{60}a+(\frac{-17}{120}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{3}+q)(\frac{17}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{-b}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{16}q+\frac{1}{3}b-\frac{1}{3}.\frac{17}{16}& \text{Uitwerken } \\ & =-bq+\frac{17}{16}q+\frac{1}{3}b-\frac{17}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{11}{17}-b)(\frac{-1}{3}+q)& =(\color{red}{-b}+\color{orange}{\frac{11}{17}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{3}b+\frac{11}{17}q-\frac{11}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =-bq+\frac{1}{3}b+\frac{11}{17}q-\frac{11}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{2}-a)((-10)+q)& =(\color{red}{-a}+\color{orange}{\frac{-11}{2}}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-10)} + \color{orange}{(\frac{-11}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -aq+10a-\frac{11}{2}q+\frac{11}{2}.10& \text{Uitwerken } \\ & =-aq+10a-\frac{11}{2}q+\frac{110}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+10a-\frac{11}{2}q+55 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{11}{4})(\frac{1}{6}+p)& =(\color{red}{p}+\color{orange}{\frac{11}{4}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{11}{4})} . \color{green}{(p)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{6}p+\frac{11}{4}p+\frac{11}{4}.\frac{1}{6}& \text{Uitwerken } \\ & =p^2+(\frac{1}{6}+\frac{11}{4})p+\frac{11}{24} & \text{Neem samen} \\ &=p^2+\frac{35}{12}p+\frac{11}{24} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b-\frac{5}{17})(p-\frac{-7}{18})& =(\color{red}{b}+\color{orange}{\frac{-5}{17}}).(\color{green}{p}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{18}b-\frac{5}{17}p-\frac{5}{17}.\frac{7}{18}& \text{Uitwerken } \\ & =bp+\frac{7}{18}b-\frac{5}{17}p-\frac{35}{306} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-1}{9}+p)(b-\frac{-12}{12})& =(\color{red}{p}+\color{orange}{\frac{-1}{9}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-\frac{1}{9}b-\frac{1}{9}.1& \text{Uitwerken } \\ & =bp+1p-\frac{1}{9}b-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{17}{20}-b)(q-(-17))& =(\color{red}{-b}+\color{orange}{\frac{17}{20}}).(\color{green}{q}+\color{blue}{17})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(17)} + \color{orange}{(\frac{17}{20})} . \color{green}{(q)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = -bq-17b+\frac{17}{20}q+\frac{17}{20}.17& \text{Uitwerken } \\ & =-bq-17b+\frac{17}{20}q+\frac{289}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{11}{11}-b)(\frac{4}{15}-p)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{15}b-1p+1.\frac{4}{15}& \text{Uitwerken } \\ & =bp-\frac{4}{15}b-1p+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-15 09:01:35
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