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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{4}{8})(\frac{12}{5}-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{-q}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{12}{5}b+\frac{1}{2}q-\frac{1}{2}.\frac{12}{5}& \text{Uitwerken } \\ & =-bq+\frac{12}{5}b+\frac{1}{2}q-\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{12}{5}b+\frac{1}{2}q-\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{13}-a)(p+\frac{3}{5})& =(\color{red}{-a}+\color{orange}{\frac{-14}{13}}).(\color{green}{p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{5}a-\frac{14}{13}p-\frac{14}{13}.\frac{3}{5}& \text{Uitwerken } \\ & =-ap-\frac{3}{5}a-\frac{14}{13}p-\frac{42}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{10}{18})(a+\frac{-2}{9})& =(\color{red}{x}+\color{orange}{\frac{-5}{9}}).(\color{green}{a}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{9}x-\frac{5}{9}a+\frac{5}{9}.\frac{2}{9}& \text{Uitwerken } \\ & =ax-\frac{2}{9}x-\frac{5}{9}a+\frac{10}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-10}{19})(\frac{19}{2}+b)& =(\color{red}{q}+\color{orange}{\frac{-10}{19}}).(\color{green}{b}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{2}q-\frac{10}{19}b-\frac{10}{19}.\frac{19}{2}& \text{Uitwerken } \\ & =bq+\frac{19}{2}q-\frac{10}{19}b-\frac{190}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{19}{2}q-\frac{10}{19}b-5 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{14}{19})((-15)-x)& =(\color{red}{q}+\color{orange}{\frac{-14}{19}}).(\color{green}{-x}+\color{blue}{(-15)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-15)} + \color{orange}{(\frac{-14}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -qx-15q+\frac{14}{19}x+\frac{14}{19}.15& \text{Uitwerken } \\ & =-qx-15q+\frac{14}{19}x+\frac{210}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{6}+b)(\frac{19}{15}-b)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{-b}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(-3)} . \color{green}{(-b)} + \color{orange}{(-3)} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{19}{15}b+3b-3.\frac{19}{15}& \text{Uitwerken } \\ & =-b^2+(\frac{19}{15}+3)b-\frac{57}{15} & \text{Neem samen} \\ &=-b^2+\frac{64}{15}b-\frac{57}{15} & \text{Maak de som} \\ &=-b^2+\frac{64}{15}b-\frac{19}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-4}{16})(\frac{-5}{7}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{7}b+\frac{1}{4}x-\frac{1}{4}.\frac{5}{7}& \text{Uitwerken } \\ & =bx-\frac{5}{7}b+\frac{1}{4}x-\frac{5}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{5}-a)(\frac{-9}{20}-a)& =(\color{red}{-a}+\color{orange}{\frac{11}{5}}).(\color{green}{-a}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{11}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{20}a-\frac{11}{5}a-\frac{11}{5}.\frac{9}{20}& \text{Uitwerken } \\ & =a^2+(\frac{9}{20}+(\frac{-11}{5}))a-(\frac{-99}{100}) & \text{Neem samen} \\ &=a^2-\frac{35}{20}a-(\frac{-99}{100}) & \text{Maak de som} \\ &=a^2-\frac{7}{4}a+\frac{99}{100} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-12}{2}-b)(\frac{8}{6}+q)& =(\color{red}{-b}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{3}b-6q-6.\frac{4}{3}& \text{Uitwerken } \\ & =-bq-\frac{4}{3}b-6q-\frac{24}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{4}{3}b-6q-8 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-1}{17})(\frac{8}{13}+p)& =(\color{red}{b}+\color{orange}{\frac{1}{17}}).(\color{green}{p}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{1}{17})} . \color{green}{(p)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{13}b+\frac{1}{17}p+\frac{1}{17}.\frac{8}{13}& \text{Uitwerken } \\ & =bp+\frac{8}{13}b+\frac{1}{17}p+\frac{8}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{19}{2})(\frac{14}{11}-q)& =(\color{red}{a}+\color{orange}{\frac{19}{2}}).(\color{green}{-q}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{19}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{14}{11}a-\frac{19}{2}q+\frac{19}{2}.\frac{14}{11}& \text{Uitwerken } \\ & =-aq+\frac{14}{11}a-\frac{19}{2}q+\frac{266}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{14}{11}a-\frac{19}{2}q+\frac{133}{11} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{8}+q)(\frac{-11}{10}-q)& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{-q}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{11}{10}q+\frac{1}{4}q+\frac{1}{4}.\frac{11}{10}& \text{Uitwerken } \\ & =-q^2+((\frac{-11}{10})+\frac{1}{4})q+(\frac{-11}{40}) & \text{Neem samen} \\ &=-q^2-\frac{17}{20}q+(\frac{-11}{40}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-25 02:05:39
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