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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-20}{3})(q+\frac{1}{11})& =(\color{red}{a}+\color{orange}{\frac{20}{3}}).(\color{green}{q}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{20}{3})} . \color{green}{(q)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{11}a+\frac{20}{3}q+\frac{20}{3}.\frac{1}{11}& \text{Uitwerken } \\ & =aq+\frac{1}{11}a+\frac{20}{3}q+\frac{20}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{5}-x)(q+\frac{19}{6})& =(\color{red}{-x}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{6}x+\frac{3}{5}q+\frac{3}{5}.\frac{19}{6}& \text{Uitwerken } \\ & =-qx-\frac{19}{6}x+\frac{3}{5}q+\frac{57}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{19}{6}x+\frac{3}{5}q+\frac{19}{10} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-1}{8}-b)(b-\frac{-2}{6})& =(\color{red}{-b}+\color{orange}{\frac{-1}{8}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{3}b-\frac{1}{8}b-\frac{1}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{3})+(\frac{-1}{8}))b-\frac{1}{24} & \text{Neem samen} \\ &=-b^2-\frac{11}{24}b-\frac{1}{24} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{6}+a)(\frac{10}{13}+q)& =(\color{red}{a}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{13}a-\frac{5}{6}q-\frac{5}{6}.\frac{10}{13}& \text{Uitwerken } \\ & =aq+\frac{10}{13}a-\frac{5}{6}q-\frac{50}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{13}a-\frac{5}{6}q-\frac{25}{39} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{7}+p)(\frac{17}{20}-a)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{20}p-2a+2.\frac{17}{20}& \text{Uitwerken } \\ & =-ap+\frac{17}{20}p-2a+\frac{34}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{17}{20}p-2a+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-(-16))(x-10)& =(\color{red}{b}+\color{orange}{16}).(\color{green}{x}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-10)} + \color{orange}{(16)} . \color{green}{(x)} + \color{orange}{(16)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = bx-10b+16x-16.10& \text{Uitwerken } \\ & =bx-10b+16x-160 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-19}{9})(a-\frac{-19}{19})& =(\color{red}{q}+\color{orange}{\frac{-19}{9}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1q-\frac{19}{9}a-\frac{19}{9}.1& \text{Uitwerken } \\ & =aq+1q-\frac{19}{9}a-\frac{19}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{9}{3})(p+\frac{-19}{9})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{9}a-3p+3.\frac{19}{9}& \text{Uitwerken } \\ & =ap-\frac{19}{9}a-3p+\frac{57}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{9}a-3p+\frac{19}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{13}+p)(\frac{1}{12}-q)& =(\color{red}{p}+\color{orange}{\frac{8}{13}}).(\color{green}{-q}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{8}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{12}p-\frac{8}{13}q+\frac{8}{13}.\frac{1}{12}& \text{Uitwerken } \\ & =-pq+\frac{1}{12}p-\frac{8}{13}q+\frac{8}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{1}{12}p-\frac{8}{13}q+\frac{2}{39} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{8}+a)(\frac{11}{15}-q)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{-q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{11}{15}a-\frac{1}{8}q+\frac{1}{8}.\frac{11}{15}& \text{Uitwerken } \\ & =-aq+\frac{11}{15}a-\frac{1}{8}q+\frac{11}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{19}-p)(p-\frac{16}{4})& =(\color{red}{-p}+\color{orange}{\frac{10}{19}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-4)} + \color{orange}{(\frac{10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -pp+4p+\frac{10}{19}p-\frac{10}{19}.4& \text{Uitwerken } \\ & =-p^2+(4+\frac{10}{19})p-\frac{40}{19} & \text{Neem samen} \\ &=-p^2+\frac{86}{19}p-\frac{40}{19} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q-\frac{9}{9})(b+\frac{11}{10})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{10}q-1b-1.\frac{11}{10}& \text{Uitwerken } \\ & =bq+\frac{11}{10}q-1b-\frac{11}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-08 05:46:55
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