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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-1}{5})(a+\frac{16}{5})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{16}{5}b+\frac{1}{5}a+\frac{1}{5}.\frac{16}{5}& \text{Uitwerken } \\ & =ab+\frac{16}{5}b+\frac{1}{5}a+\frac{16}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{9}+q)(\frac{14}{16}+p)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{8}q-\frac{4}{3}p-\frac{4}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =pq+\frac{7}{8}q-\frac{4}{3}p-\frac{28}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{7}{8}q-\frac{4}{3}p-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-3}{15})(\frac{19}{17}+b)& =(\color{red}{q}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{17}q-\frac{1}{5}b-\frac{1}{5}.\frac{19}{17}& \text{Uitwerken } \\ & =bq+\frac{19}{17}q-\frac{1}{5}b-\frac{19}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{8}{15})(\frac{1}{3}-x)& =(\color{red}{b}+\color{orange}{\frac{-8}{15}}).(\color{green}{-x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{3}b+\frac{8}{15}x-\frac{8}{15}.\frac{1}{3}& \text{Uitwerken } \\ & =-bx+\frac{1}{3}b+\frac{8}{15}x-\frac{8}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{20}+a)(x+\frac{9}{6})& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}a+\frac{13}{20}x+\frac{13}{20}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}a+\frac{13}{20}x+\frac{39}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{13}-a)(b-\frac{14}{2})& =(\color{red}{-a}+\color{orange}{\frac{2}{13}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(-7)} + \color{orange}{(\frac{2}{13})} . \color{green}{(b)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -ab+7a+\frac{2}{13}b-\frac{2}{13}.7& \text{Uitwerken } \\ & =-ab+7a+\frac{2}{13}b-\frac{14}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{5}-q)(\frac{-8}{15}+p)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{8}{15}q+1p-1.\frac{8}{15}& \text{Uitwerken } \\ & =-pq+\frac{8}{15}q+1p-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{19}{18})(\frac{13}{16}+a)& =(\color{red}{a}+\color{orange}{\frac{19}{18}}).(\color{green}{a}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{19}{18})} . \color{green}{(a)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{13}{16}a+\frac{19}{18}a+\frac{19}{18}.\frac{13}{16}& \text{Uitwerken } \\ & =a^2+(\frac{13}{16}+\frac{19}{18})a+\frac{247}{288} & \text{Neem samen} \\ &=a^2+\frac{269}{144}a+\frac{247}{288} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(x-\frac{5}{5})(b-\frac{-18}{4})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{2}x-1b-1.\frac{9}{2}& \text{Uitwerken } \\ & =bx+\frac{9}{2}x-1b-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{19}-p)(q+\frac{-14}{5})& =(\color{red}{-p}+\color{orange}{\frac{-15}{19}}).(\color{green}{q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{14}{5}p-\frac{15}{19}q+\frac{15}{19}.\frac{14}{5}& \text{Uitwerken } \\ & =-pq+\frac{14}{5}p-\frac{15}{19}q+\frac{210}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{14}{5}p-\frac{15}{19}q+\frac{42}{19} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{18}-q)(\frac{-4}{14}-b)& =(\color{red}{-q}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{7}q+\frac{10}{9}b+\frac{10}{9}.\frac{2}{7}& \text{Uitwerken } \\ & =bq+\frac{2}{7}q+\frac{10}{9}b+\frac{20}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-1}{9})(\frac{19}{13}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{9}}).(\color{green}{-p}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{1}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{13}a-\frac{1}{9}p+\frac{1}{9}.\frac{19}{13}& \text{Uitwerken } \\ & =-ap+\frac{19}{13}a-\frac{1}{9}p+\frac{19}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-13 02:31:30
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