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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-15}{20})(\frac{17}{11}+a)& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{17}{11}a-\frac{3}{4}a-\frac{3}{4}.\frac{17}{11}& \text{Uitwerken } \\ & =a^2+(\frac{17}{11}+(\frac{-3}{4}))a-(\frac{-51}{44}) & \text{Neem samen} \\ &=a^2+\frac{35}{44}a-(\frac{-51}{44}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{8}+x)(p+\frac{-6}{14})& =(\color{red}{x}+\color{orange}{\frac{9}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{7}x+\frac{9}{4}p-\frac{9}{4}.\frac{3}{7}& \text{Uitwerken } \\ & =px-\frac{3}{7}x+\frac{9}{4}p-\frac{27}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{3}-p)(\frac{10}{14}-x)& =(\color{red}{-p}+\color{orange}{\frac{-11}{3}}).(\color{green}{-x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{7}p+\frac{11}{3}x-\frac{11}{3}.\frac{5}{7}& \text{Uitwerken } \\ & =px-\frac{5}{7}p+\frac{11}{3}x-\frac{55}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-6}{19})(\frac{8}{6}+a)& =(\color{red}{x}+\color{orange}{\frac{6}{19}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{6}{19})} . \color{green}{(a)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{3}x+\frac{6}{19}a+\frac{6}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =ax+\frac{4}{3}x+\frac{6}{19}a+\frac{24}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{4}{3}x+\frac{6}{19}a+\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-5}{19})(a-\frac{-13}{10})& =(\color{red}{q}+\color{orange}{\frac{5}{19}}).(\color{green}{a}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{10}q+\frac{5}{19}a+\frac{5}{19}.\frac{13}{10}& \text{Uitwerken } \\ & =aq+\frac{13}{10}q+\frac{5}{19}a+\frac{65}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{13}{10}q+\frac{5}{19}a+\frac{13}{38} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{1}{5})(\frac{4}{5}+b)& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{5}p+\frac{1}{5}b+\frac{1}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =bp+\frac{4}{5}p+\frac{1}{5}b+\frac{4}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-17}{14})(\frac{-10}{13}-x)& =(\color{red}{a}+\color{orange}{\frac{-17}{14}}).(\color{green}{-x}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{10}{13}a+\frac{17}{14}x+\frac{17}{14}.\frac{10}{13}& \text{Uitwerken } \\ & =-ax-\frac{10}{13}a+\frac{17}{14}x+\frac{170}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{10}{13}a+\frac{17}{14}x+\frac{85}{91} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{9}{15})(b+\frac{3}{6})& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x-\frac{3}{5}b-\frac{3}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x-\frac{3}{5}b-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{7}-x)(q-\frac{-13}{14})& =(\color{red}{-x}+\color{orange}{\frac{-16}{7}}).(\color{green}{q}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{14}x-\frac{16}{7}q-\frac{16}{7}.\frac{13}{14}& \text{Uitwerken } \\ & =-qx-\frac{13}{14}x-\frac{16}{7}q-\frac{208}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{13}{14}x-\frac{16}{7}q-\frac{104}{49} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{4}{18})(\frac{12}{13}-b)& =(\color{red}{a}+\color{orange}{\frac{-2}{9}}).(\color{green}{-b}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{12}{13}a+\frac{2}{9}b-\frac{2}{9}.\frac{12}{13}& \text{Uitwerken } \\ & =-ab+\frac{12}{13}a+\frac{2}{9}b-\frac{24}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{12}{13}a+\frac{2}{9}b-\frac{8}{39} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q-\frac{11}{15})(x-\frac{-11}{11})& =(\color{red}{q}+\color{orange}{\frac{-11}{15}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1q-\frac{11}{15}x-\frac{11}{15}.1& \text{Uitwerken } \\ & =qx+1q-\frac{11}{15}x-\frac{11}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-16}{16})(\frac{-11}{2}+x)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{2}b+1x-1.\frac{11}{2}& \text{Uitwerken } \\ & =bx-\frac{11}{2}b+1x-\frac{11}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-26 07:31:27
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