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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{6}-b)(\frac{20}{3}-a)& =(\color{red}{-b}+\color{orange}{\frac{-19}{6}}).(\color{green}{-a}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{20}{3}b+\frac{19}{6}a-\frac{19}{6}.\frac{20}{3}& \text{Uitwerken } \\ & =ab-\frac{20}{3}b+\frac{19}{6}a-\frac{380}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{20}{3}b+\frac{19}{6}a-\frac{190}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{9}{15}+b)(a-\frac{-3}{12})& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{4}b+\frac{3}{5}a+\frac{3}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =ab+\frac{1}{4}b+\frac{3}{5}a+\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-3}{9}-q)(p+\frac{1}{3})& =(\color{red}{-q}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{3}q-\frac{1}{3}p-\frac{1}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =-pq-\frac{1}{3}q-\frac{1}{3}p-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-11}{17}+p)(x+19)& =(\color{red}{p}+\color{orange}{\frac{-11}{17}}).(\color{green}{x}+\color{blue}{19})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(19)} + \color{orange}{(\frac{-11}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = px+19p-\frac{11}{17}x-\frac{11}{17}.19& \text{Uitwerken } \\ & =px+19p-\frac{11}{17}x-\frac{209}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{11}{14})(\frac{3}{9}+a)& =(\color{red}{a}+\color{orange}{\frac{-11}{14}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{3}a-\frac{11}{14}a-\frac{11}{14}.\frac{1}{3}& \text{Uitwerken } \\ & =a^2+(\frac{1}{3}+(\frac{-11}{14}))a-(\frac{-11}{42}) & \text{Neem samen} \\ &=a^2-\frac{19}{42}a-(\frac{-11}{42}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{8}{13}-p)(x-\frac{-3}{15})& =(\color{red}{-p}+\color{orange}{\frac{8}{13}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{8}{13})} . \color{green}{(x)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{5}p+\frac{8}{13}x+\frac{8}{13}.\frac{1}{5}& \text{Uitwerken } \\ & =-px-\frac{1}{5}p+\frac{8}{13}x+\frac{8}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{17}+a)(b-\frac{18}{3})& =(\color{red}{a}+\color{orange}{\frac{3}{17}}).(\color{green}{b}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-6)} + \color{orange}{(\frac{3}{17})} . \color{green}{(b)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ab-6a+\frac{3}{17}b-\frac{3}{17}.6& \text{Uitwerken } \\ & =ab-6a+\frac{3}{17}b-\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-13}{18})(\frac{-18}{19}-q)& =(\color{red}{x}+\color{orange}{\frac{13}{18}}).(\color{green}{-q}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{13}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{18}{19}x-\frac{13}{18}q-\frac{13}{18}.\frac{18}{19}& \text{Uitwerken } \\ & =-qx-\frac{18}{19}x-\frac{13}{18}q-\frac{234}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{18}{19}x-\frac{13}{18}q-\frac{13}{19} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-16}{3})(\frac{-13}{12}-p)& =(\color{red}{b}+\color{orange}{\frac{16}{3}}).(\color{green}{-p}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{16}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{12}b-\frac{16}{3}p-\frac{16}{3}.\frac{13}{12}& \text{Uitwerken } \\ & =-bp-\frac{13}{12}b-\frac{16}{3}p-\frac{208}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{13}{12}b-\frac{16}{3}p-\frac{52}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{19}-x)(\frac{6}{11}+p)& =(\color{red}{-x}+\color{orange}{\frac{-16}{19}}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{6}{11}x-\frac{16}{19}p-\frac{16}{19}.\frac{6}{11}& \text{Uitwerken } \\ & =-px-\frac{6}{11}x-\frac{16}{19}p-\frac{96}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{19}-a)(q-\frac{-10}{9})& =(\color{red}{-a}+\color{orange}{\frac{18}{19}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{18}{19})} . \color{green}{(q)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{10}{9}a+\frac{18}{19}q+\frac{18}{19}.\frac{10}{9}& \text{Uitwerken } \\ & =-aq-\frac{10}{9}a+\frac{18}{19}q+\frac{180}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{10}{9}a+\frac{18}{19}q+\frac{20}{19} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-11}{3})(b-\frac{11}{18})& =(\color{red}{q}+\color{orange}{\frac{-11}{3}}).(\color{green}{b}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{18}q-\frac{11}{3}b+\frac{11}{3}.\frac{11}{18}& \text{Uitwerken } \\ & =bq-\frac{11}{18}q-\frac{11}{3}b+\frac{121}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-18 19:02:29
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