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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{12}-x)(\frac{1}{13}-p)& =(\color{red}{-x}+\color{orange}{\frac{-1}{3}}).(\color{green}{-p}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{13}x+\frac{1}{3}p-\frac{1}{3}.\frac{1}{13}& \text{Uitwerken } \\ & =px-\frac{1}{13}x+\frac{1}{3}p-\frac{1}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{2}{2})(b+\frac{3}{5})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{5}q-1b-1.\frac{3}{5}& \text{Uitwerken } \\ & =bq+\frac{3}{5}q-1b-\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{12}-b)(q+\frac{16}{15})& =(\color{red}{-b}+\color{orange}{\frac{-19}{12}}).(\color{green}{q}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{15}b-\frac{19}{12}q-\frac{19}{12}.\frac{16}{15}& \text{Uitwerken } \\ & =-bq-\frac{16}{15}b-\frac{19}{12}q-\frac{304}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{16}{15}b-\frac{19}{12}q-\frac{76}{45} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p+5)(b+\frac{9}{20})& =(\color{red}{p}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{20}p+5b+5.\frac{9}{20}& \text{Uitwerken } \\ & =bp+\frac{9}{20}p+5b+\frac{45}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{20}p+5b+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-10}{19})(\frac{-18}{6}+q)& =(\color{red}{x}+\color{orange}{\frac{-10}{19}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-10}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = qx-3x-\frac{10}{19}q+\frac{10}{19}.3& \text{Uitwerken } \\ & =qx-3x-\frac{10}{19}q+\frac{30}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{10}{18}-p)(\frac{-18}{11}-a)& =(\color{red}{-p}+\color{orange}{\frac{5}{9}}).(\color{green}{-a}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{5}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{18}{11}p-\frac{5}{9}a-\frac{5}{9}.\frac{18}{11}& \text{Uitwerken } \\ & =ap+\frac{18}{11}p-\frac{5}{9}a-\frac{90}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{18}{11}p-\frac{5}{9}a-\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-10}{16})(\frac{14}{2}-x)& =(\color{red}{b}+\color{orange}{\frac{-5}{8}}).(\color{green}{-x}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(7)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -bx+7b+\frac{5}{8}x-\frac{5}{8}.7& \text{Uitwerken } \\ & =-bx+7b+\frac{5}{8}x-\frac{35}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{4}-p)(x-\frac{4}{5})& =(\color{red}{-p}+\color{orange}{\frac{-7}{2}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{4}{5}p-\frac{7}{2}x+\frac{7}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-px+\frac{4}{5}p-\frac{7}{2}x+\frac{28}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{4}{5}p-\frac{7}{2}x+\frac{14}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-3}{16})(\frac{-15}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{3}{16}}).(\color{green}{p}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{4}a+\frac{3}{16}p-\frac{3}{16}.\frac{15}{4}& \text{Uitwerken } \\ & =ap-\frac{15}{4}a+\frac{3}{16}p-\frac{45}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{11}-p)(\frac{4}{16}-x)& =(\color{red}{-p}+\color{orange}{\frac{15}{11}}).(\color{green}{-x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{15}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{4}p-\frac{15}{11}x+\frac{15}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =px-\frac{1}{4}p-\frac{15}{11}x+\frac{15}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-14}{5})(\frac{8}{17}-q)& =(\color{red}{b}+\color{orange}{\frac{-14}{5}}).(\color{green}{-q}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{17}b+\frac{14}{5}q-\frac{14}{5}.\frac{8}{17}& \text{Uitwerken } \\ & =-bq+\frac{8}{17}b+\frac{14}{5}q-\frac{112}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{13}-b)(a+\frac{14}{7})& =(\color{red}{-b}+\color{orange}{\frac{18}{13}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(2)} + \color{orange}{(\frac{18}{13})} . \color{green}{(a)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ab-2b+\frac{18}{13}a+\frac{18}{13}.2& \text{Uitwerken } \\ & =-ab-2b+\frac{18}{13}a+\frac{36}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-14 13:06:38
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