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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{17}{4})(x-\frac{13}{10})& =(\color{red}{q}+\color{orange}{\frac{-17}{4}}).(\color{green}{x}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{10}q-\frac{17}{4}x+\frac{17}{4}.\frac{13}{10}& \text{Uitwerken } \\ & =qx-\frac{13}{10}q-\frac{17}{4}x+\frac{221}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-15}{16})(\frac{10}{5}-q)& =(\color{red}{q}+\color{orange}{\frac{15}{16}}).(\color{green}{-q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{15}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qq+2q-\frac{15}{16}q+\frac{15}{16}.2& \text{Uitwerken } \\ & =-q^2+(2+(\frac{-15}{16}))q+(\frac{-30}{16}) & \text{Neem samen} \\ &=-q^2+\frac{17}{16}q+(\frac{-30}{16}) & \text{Maak de som} \\ &=-q^2+\frac{17}{16}q+(\frac{-15}{8}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{14}+b)(\frac{-18}{8}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{7}}).(\color{green}{x}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{1}{7})} . \color{green}{(x)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{4}b+\frac{1}{7}x-\frac{1}{7}.\frac{9}{4}& \text{Uitwerken } \\ & =bx-\frac{9}{4}b+\frac{1}{7}x-\frac{9}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{15}{12})(\frac{-3}{17}+b)& =(\color{red}{b}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{17}b-\frac{5}{4}b+\frac{5}{4}.\frac{3}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{17})+(\frac{-5}{4}))b+\frac{15}{68} & \text{Neem samen} \\ &=b^2-\frac{97}{68}b+\frac{15}{68} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-11}{17})(q+\frac{4}{19})& =(\color{red}{a}+\color{orange}{\frac{11}{17}}).(\color{green}{q}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{19}a+\frac{11}{17}q+\frac{11}{17}.\frac{4}{19}& \text{Uitwerken } \\ & =aq+\frac{4}{19}a+\frac{11}{17}q+\frac{44}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{16}{13})(\frac{19}{15}+b)& =(\color{red}{p}+\color{orange}{\frac{-16}{13}}).(\color{green}{b}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{15}p-\frac{16}{13}b-\frac{16}{13}.\frac{19}{15}& \text{Uitwerken } \\ & =bp+\frac{19}{15}p-\frac{16}{13}b-\frac{304}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-17}{7})(p+\frac{-15}{16})& =(\color{red}{b}+\color{orange}{\frac{17}{7}}).(\color{green}{p}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{17}{7})} . \color{green}{(p)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{15}{16}b+\frac{17}{7}p-\frac{17}{7}.\frac{15}{16}& \text{Uitwerken } \\ & =bp-\frac{15}{16}b+\frac{17}{7}p-\frac{255}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{1}{5})(\frac{11}{17}-x)& =(\color{red}{a}+\color{orange}{\frac{1}{5}}).(\color{green}{-x}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{17}a-\frac{1}{5}x+\frac{1}{5}.\frac{11}{17}& \text{Uitwerken } \\ & =-ax+\frac{11}{17}a-\frac{1}{5}x+\frac{11}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{7}{13})(\frac{-2}{20}+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{13}}).(\color{green}{p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{10}p-\frac{7}{13}p+\frac{7}{13}.\frac{1}{10}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{10})+(\frac{-7}{13}))p+\frac{7}{130} & \text{Neem samen} \\ &=p^2-\frac{83}{130}p+\frac{7}{130} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-15}{17})(b+\frac{4}{5})& =(\color{red}{b}+\color{orange}{\frac{-15}{17}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{5}b-\frac{15}{17}b-\frac{15}{17}.\frac{4}{5}& \text{Uitwerken } \\ & =b^2+(\frac{4}{5}+(\frac{-15}{17}))b-(\frac{-60}{85}) & \text{Neem samen} \\ &=b^2-\frac{7}{85}b-(\frac{-60}{85}) & \text{Maak de som} \\ &=b^2-\frac{7}{85}b+\frac{12}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(p-\frac{16}{3})(b+\frac{-18}{3})& =(\color{red}{p}+\color{orange}{\frac{-16}{3}}).(\color{green}{b}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-6)} + \color{orange}{(\frac{-16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = bp-6p-\frac{16}{3}b+\frac{16}{3}.6& \text{Uitwerken } \\ & =bp-6p-\frac{16}{3}b+\frac{96}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-6p-\frac{16}{3}b+32 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{20}{9}-q)(a-\frac{4}{11})& =(\color{red}{-q}+\color{orange}{\frac{20}{9}}).(\color{green}{a}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{20}{9})} . \color{green}{(a)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{11}q+\frac{20}{9}a-\frac{20}{9}.\frac{4}{11}& \text{Uitwerken } \\ & =-aq+\frac{4}{11}q+\frac{20}{9}a-\frac{80}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-18 16:05:39
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