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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{20}+x)(q+(-2))& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2x+\frac{1}{5}q-\frac{1}{5}.2& \text{Uitwerken } \\ & =qx-2x+\frac{1}{5}q-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{9}{20})(a+\frac{-5}{2})& =(\color{red}{q}+\color{orange}{\frac{-9}{20}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{2}q-\frac{9}{20}a+\frac{9}{20}.\frac{5}{2}& \text{Uitwerken } \\ & =aq-\frac{5}{2}q-\frac{9}{20}a+\frac{45}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{2}q-\frac{9}{20}a+\frac{9}{8} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-2}{13})(\frac{-4}{5}-q)& =(\color{red}{x}+\color{orange}{\frac{2}{13}}).(\color{green}{-q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{2}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{5}x-\frac{2}{13}q-\frac{2}{13}.\frac{4}{5}& \text{Uitwerken } \\ & =-qx-\frac{4}{5}x-\frac{2}{13}q-\frac{8}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+18)(5+a)& =(\color{red}{p}+\color{orange}{18}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(18)} . \color{green}{(a)} + \color{orange}{(18)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ap+5p+18a+18.5& \text{Uitwerken } \\ & =ap+5p+18a+90 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+(-16))(b+\frac{5}{3})& =(\color{red}{x}+\color{orange}{(-16)}).(\color{green}{b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(-16)} . \color{green}{(b)} + \color{orange}{(-16)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{3}x-16b-16.\frac{5}{3}& \text{Uitwerken } \\ & =bx+\frac{5}{3}x-16b-\frac{80}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{8}+x)(x-\frac{-20}{4})& =(\color{red}{x}+\color{orange}{\frac{7}{8}}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = xx+5x+\frac{7}{8}x+\frac{7}{8}.5& \text{Uitwerken } \\ & =x^2+(5+\frac{7}{8})x+\frac{35}{8} & \text{Neem samen} \\ &=x^2+\frac{47}{8}x+\frac{35}{8} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(19+x)(\frac{10}{14}+q)& =(\color{red}{x}+\color{orange}{19}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(19)} . \color{green}{(q)} + \color{orange}{(19)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{7}x+19q+19.\frac{5}{7}& \text{Uitwerken } \\ & =qx+\frac{5}{7}x+19q+\frac{95}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{17}{18})(\frac{1}{6}+p)& =(\color{red}{b}+\color{orange}{\frac{17}{18}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{17}{18})} . \color{green}{(p)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{6}b+\frac{17}{18}p+\frac{17}{18}.\frac{1}{6}& \text{Uitwerken } \\ & =bp+\frac{1}{6}b+\frac{17}{18}p+\frac{17}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-4}{3})(p-\frac{-16}{12})& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{3}b-\frac{4}{3}p-\frac{4}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =bp+\frac{4}{3}b-\frac{4}{3}p-\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{12}{18})(a+\frac{9}{16})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{16}p+\frac{2}{3}a+\frac{2}{3}.\frac{9}{16}& \text{Uitwerken } \\ & =ap+\frac{9}{16}p+\frac{2}{3}a+\frac{18}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{16}p+\frac{2}{3}a+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-7}{19})(q+\frac{-7}{3})& =(\color{red}{b}+\color{orange}{\frac{7}{19}}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{3}b+\frac{7}{19}q-\frac{7}{19}.\frac{7}{3}& \text{Uitwerken } \\ & =bq-\frac{7}{3}b+\frac{7}{19}q-\frac{49}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-11}{5})(p-\frac{-13}{17})& =(\color{red}{p}+\color{orange}{\frac{-11}{5}}).(\color{green}{p}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{17}p-\frac{11}{5}p-\frac{11}{5}.\frac{13}{17}& \text{Uitwerken } \\ & =p^2+(\frac{13}{17}+(\frac{-11}{5}))p-(\frac{-143}{85}) & \text{Neem samen} \\ &=p^2-\frac{122}{85}p-(\frac{-143}{85}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-07 17:46:48
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