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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-18}{16})(\frac{10}{19}+q)& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{10}{19}b-\frac{9}{8}q-\frac{9}{8}.\frac{10}{19}& \text{Uitwerken } \\ & =bq+\frac{10}{19}b-\frac{9}{8}q-\frac{90}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{10}{19}b-\frac{9}{8}q-\frac{45}{76} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{11}{15})(\frac{20}{16}-p)& =(\color{red}{p}+\color{orange}{\frac{11}{15}}).(\color{green}{-p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{11}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{5}{4}p-\frac{11}{15}p+\frac{11}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{5}{4}+(\frac{-11}{15}))p+(\frac{-55}{60}) & \text{Neem samen} \\ &=-p^2+\frac{31}{60}p+(\frac{-55}{60}) & \text{Maak de som} \\ &=-p^2+\frac{31}{60}p+(\frac{-11}{12}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{10}+b)(a-5)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ab-5b-\frac{3}{2}a+\frac{3}{2}.5& \text{Uitwerken } \\ & =ab-5b-\frac{3}{2}a+\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{6}{11}-x)(q+\frac{15}{20})& =(\color{red}{-x}+\color{orange}{\frac{6}{11}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{6}{11})} . \color{green}{(q)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{4}x+\frac{6}{11}q+\frac{6}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx-\frac{3}{4}x+\frac{6}{11}q+\frac{18}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{3}{4}x+\frac{6}{11}q+\frac{9}{22} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{18}{11})(\frac{5}{5}+q)& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1x+\frac{18}{11}q+\frac{18}{11}.1& \text{Uitwerken } \\ & =qx+1x+\frac{18}{11}q+\frac{18}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-5}{19})(a-\frac{5}{13})& =(\color{red}{a}+\color{orange}{\frac{5}{19}}).(\color{green}{a}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{13}a+\frac{5}{19}a-\frac{5}{19}.\frac{5}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{13})+\frac{5}{19})a-(\frac{-25}{247}) & \text{Neem samen} \\ &=a^2-\frac{30}{247}a-(\frac{-25}{247}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{4}-b)(b+\frac{-10}{5})& =(\color{red}{-b}+\color{orange}{\frac{-9}{4}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bb+2b-\frac{9}{4}b+\frac{9}{4}.2& \text{Uitwerken } \\ & =-b^2+(2+(\frac{-9}{4}))b+(\frac{-18}{4}) & \text{Neem samen} \\ &=-b^2-\frac{1}{4}b+(\frac{-18}{4}) & \text{Maak de som} \\ &=-b^2-\frac{1}{4}b+(\frac{-9}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{14}+a)(b-\frac{20}{17})& =(\color{red}{a}+\color{orange}{\frac{-9}{14}}).(\color{green}{b}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{20}{17}a-\frac{9}{14}b+\frac{9}{14}.\frac{20}{17}& \text{Uitwerken } \\ & =ab-\frac{20}{17}a-\frac{9}{14}b+\frac{180}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{20}{17}a-\frac{9}{14}b+\frac{90}{119} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{15}{18})(q-\frac{14}{14})& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b+\frac{5}{6}q-\frac{5}{6}.1& \text{Uitwerken } \\ & =bq-1b+\frac{5}{6}q-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-14}{12})(a+\frac{9}{3})& =(\color{red}{b}+\color{orange}{\frac{-7}{6}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{-7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ab+3b-\frac{7}{6}a-\frac{7}{6}.3& \text{Uitwerken } \\ & =ab+3b-\frac{7}{6}a-\frac{21}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+3b-\frac{7}{6}a-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{18}-p)(q+\frac{8}{13})& =(\color{red}{-p}+\color{orange}{\frac{-19}{18}}).(\color{green}{q}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{13}p-\frac{19}{18}q-\frac{19}{18}.\frac{8}{13}& \text{Uitwerken } \\ & =-pq-\frac{8}{13}p-\frac{19}{18}q-\frac{152}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{8}{13}p-\frac{19}{18}q-\frac{76}{117} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-13}{15})(p-\frac{17}{14})& =(\color{red}{x}+\color{orange}{\frac{-13}{15}}).(\color{green}{p}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{14}x-\frac{13}{15}p+\frac{13}{15}.\frac{17}{14}& \text{Uitwerken } \\ & =px-\frac{17}{14}x-\frac{13}{15}p+\frac{221}{210} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-06 16:37:19
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