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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{16}{15})(18+x)& =(\color{red}{q}+\color{orange}{\frac{16}{15}}).(\color{green}{x}+\color{blue}{18})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(18)} + \color{orange}{(\frac{16}{15})} . \color{green}{(x)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = qx+18q+\frac{16}{15}x+\frac{16}{15}.18& \text{Uitwerken } \\ & =qx+18q+\frac{16}{15}x+\frac{288}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+18q+\frac{16}{15}x+\frac{96}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-16}{19})(\frac{9}{16}+q)& =(\color{red}{b}+\color{orange}{\frac{-16}{19}}).(\color{green}{q}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{16}b-\frac{16}{19}q-\frac{16}{19}.\frac{9}{16}& \text{Uitwerken } \\ & =bq+\frac{9}{16}b-\frac{16}{19}q-\frac{144}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{9}{16}b-\frac{16}{19}q-\frac{9}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{6}{8})(\frac{-7}{4}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{4}q-\frac{3}{4}a+\frac{3}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =aq-\frac{7}{4}q-\frac{3}{4}a+\frac{21}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{10}+b)(q-\frac{-11}{7})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{7}b+2q+2.\frac{11}{7}& \text{Uitwerken } \\ & =bq+\frac{11}{7}b+2q+\frac{22}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-19}{14}-a)(a-\frac{19}{15})& =(\color{red}{-a}+\color{orange}{\frac{-19}{14}}).(\color{green}{a}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{19}{15}a-\frac{19}{14}a+\frac{19}{14}.\frac{19}{15}& \text{Uitwerken } \\ & =-a^2+(\frac{19}{15}+(\frac{-19}{14}))a+(\frac{-361}{210}) & \text{Neem samen} \\ &=-a^2-\frac{19}{210}a+(\frac{-361}{210}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(18+a)(x+\frac{-17}{12})& =(\color{red}{a}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{12}a+18x-18.\frac{17}{12}& \text{Uitwerken } \\ & =ax-\frac{17}{12}a+18x-\frac{306}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{12}a+18x-\frac{51}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{12}+b)(a+\frac{9}{3})& =(\color{red}{b}+\color{orange}{\frac{13}{12}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{13}{12})} . \color{green}{(a)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ab+3b+\frac{13}{12}a+\frac{13}{12}.3& \text{Uitwerken } \\ & =ab+3b+\frac{13}{12}a+\frac{39}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+3b+\frac{13}{12}a+\frac{13}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{16}-p)(\frac{-20}{3}-b)& =(\color{red}{-p}+\color{orange}{\frac{-11}{16}}).(\color{green}{-b}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{20}{3}p+\frac{11}{16}b+\frac{11}{16}.\frac{20}{3}& \text{Uitwerken } \\ & =bp+\frac{20}{3}p+\frac{11}{16}b+\frac{220}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{20}{3}p+\frac{11}{16}b+\frac{55}{12} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{15}{17}+q)(\frac{11}{6}+a)& =(\color{red}{q}+\color{orange}{\frac{15}{17}}).(\color{green}{a}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{15}{17})} . \color{green}{(a)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{6}q+\frac{15}{17}a+\frac{15}{17}.\frac{11}{6}& \text{Uitwerken } \\ & =aq+\frac{11}{6}q+\frac{15}{17}a+\frac{165}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{11}{6}q+\frac{15}{17}a+\frac{55}{34} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{12}-x)(3+q)& =(\color{red}{-x}+\color{orange}{\frac{-17}{12}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(\frac{-17}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -qx-3x-\frac{17}{12}q-\frac{17}{12}.3& \text{Uitwerken } \\ & =-qx-3x-\frac{17}{12}q-\frac{51}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-3x-\frac{17}{12}q-\frac{17}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{19}+x)(p+\frac{6}{6})& =(\color{red}{x}+\color{orange}{\frac{18}{19}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{18}{19})} . \color{green}{(p)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x+\frac{18}{19}p+\frac{18}{19}.1& \text{Uitwerken } \\ & =px+1x+\frac{18}{19}p+\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{14}-b)(q-\frac{17}{7})& =(\color{red}{-b}+\color{orange}{\frac{-17}{14}}).(\color{green}{q}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{7}b-\frac{17}{14}q+\frac{17}{14}.\frac{17}{7}& \text{Uitwerken } \\ & =-bq+\frac{17}{7}b-\frac{17}{14}q+\frac{289}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-21 18:11:29
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