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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{11}{18})(p-\frac{-6}{20})& =(\color{red}{a}+\color{orange}{\frac{11}{18}}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{11}{18})} . \color{green}{(p)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{10}a+\frac{11}{18}p+\frac{11}{18}.\frac{3}{10}& \text{Uitwerken } \\ & =ap+\frac{3}{10}a+\frac{11}{18}p+\frac{33}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{10}a+\frac{11}{18}p+\frac{11}{60} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-14}{2})(\frac{4}{15}+q)& =(\color{red}{b}+\color{orange}{(-7)}).(\color{green}{q}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(-7)} . \color{green}{(q)} + \color{orange}{(-7)} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{15}b-7q-7.\frac{4}{15}& \text{Uitwerken } \\ & =bq+\frac{4}{15}b-7q-\frac{28}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{11}{16})(x-\frac{-11}{6})& =(\color{red}{x}+\color{orange}{\frac{11}{16}}).(\color{green}{x}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{11}{16})} . \color{green}{(x)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{11}{6}x+\frac{11}{16}x+\frac{11}{16}.\frac{11}{6}& \text{Uitwerken } \\ & =x^2+(\frac{11}{6}+\frac{11}{16})x+\frac{121}{96} & \text{Neem samen} \\ &=x^2+\frac{121}{48}x+\frac{121}{96} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-9}{2})(\frac{-19}{11}-b)& =(\color{red}{b}+\color{orange}{\frac{-9}{2}}).(\color{green}{-b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{11}b+\frac{9}{2}b+\frac{9}{2}.\frac{19}{11}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{11})+\frac{9}{2})b+(\frac{-171}{22}) & \text{Neem samen} \\ &=-b^2+\frac{61}{22}b+(\frac{-171}{22}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-10}{3})(p+\frac{-13}{10})& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{10}a+\frac{10}{3}p-\frac{10}{3}.\frac{13}{10}& \text{Uitwerken } \\ & =ap-\frac{13}{10}a+\frac{10}{3}p-\frac{130}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{13}{10}a+\frac{10}{3}p-\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{13}{17}-b)(\frac{15}{2}+q)& =(\color{red}{-b}+\color{orange}{\frac{13}{17}}).(\color{green}{q}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{15}{2}b+\frac{13}{17}q+\frac{13}{17}.\frac{15}{2}& \text{Uitwerken } \\ & =-bq-\frac{15}{2}b+\frac{13}{17}q+\frac{195}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-12}{15})(p+\frac{20}{19})& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{20}{19}b-\frac{4}{5}p-\frac{4}{5}.\frac{20}{19}& \text{Uitwerken } \\ & =bp+\frac{20}{19}b-\frac{4}{5}p-\frac{80}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{20}{19}b-\frac{4}{5}p-\frac{16}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{15}-q)(a-\frac{18}{6})& =(\color{red}{-q}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aq+3q-\frac{1}{3}a+\frac{1}{3}.3& \text{Uitwerken } \\ & =-aq+3q-\frac{1}{3}a+\frac{3}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+3q-\frac{1}{3}a+1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-6}{12})(x-\frac{14}{11})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{11}q+\frac{1}{2}x-\frac{1}{2}.\frac{14}{11}& \text{Uitwerken } \\ & =qx-\frac{14}{11}q+\frac{1}{2}x-\frac{14}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{14}{11}q+\frac{1}{2}x-\frac{7}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-6}{18})(\frac{-10}{16}-a)& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{-a}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{8}q-\frac{1}{3}a-\frac{1}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =-aq-\frac{5}{8}q-\frac{1}{3}a-\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{10}{13})(\frac{12}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{-10}{13}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{-10}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3a-\frac{10}{13}p-\frac{10}{13}.3& \text{Uitwerken } \\ & =ap+3a-\frac{10}{13}p-\frac{30}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{16}{14})(q+\frac{2}{9})& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{9}b+\frac{8}{7}q+\frac{8}{7}.\frac{2}{9}& \text{Uitwerken } \\ & =bq+\frac{2}{9}b+\frac{8}{7}q+\frac{16}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-24 13:32:27
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