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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{2}+p)(\frac{-4}{9}-q)& =(\color{red}{p}+\color{orange}{\frac{15}{2}}).(\color{green}{-q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{15}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{9}p-\frac{15}{2}q-\frac{15}{2}.\frac{4}{9}& \text{Uitwerken } \\ & =-pq-\frac{4}{9}p-\frac{15}{2}q-\frac{60}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{4}{9}p-\frac{15}{2}q-\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{17}{12}+x)(\frac{-19}{12}-q)& =(\color{red}{x}+\color{orange}{\frac{17}{12}}).(\color{green}{-q}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{17}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{12}x-\frac{17}{12}q-\frac{17}{12}.\frac{19}{12}& \text{Uitwerken } \\ & =-qx-\frac{19}{12}x-\frac{17}{12}q-\frac{323}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{4}{6})(a-\frac{5}{15})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{3}p-\frac{2}{3}a+\frac{2}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =ap-\frac{1}{3}p-\frac{2}{3}a+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-1}{9})(q-\frac{15}{19})& =(\color{red}{a}+\color{orange}{\frac{-1}{9}}).(\color{green}{q}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{19}a-\frac{1}{9}q+\frac{1}{9}.\frac{15}{19}& \text{Uitwerken } \\ & =aq-\frac{15}{19}a-\frac{1}{9}q+\frac{15}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{15}{19}a-\frac{1}{9}q+\frac{5}{57} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{15}{3}-x)(\frac{17}{6}+x)& =(\color{red}{-x}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{17}{6}x+5x+5.\frac{17}{6}& \text{Uitwerken } \\ & =-x^2+((\frac{-17}{6})+5)x+(\frac{-85}{6}) & \text{Neem samen} \\ &=-x^2+\frac{13}{6}x+(\frac{-85}{6}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{8}+x)(a-16)& =(\color{red}{x}+\color{orange}{\frac{-19}{8}}).(\color{green}{a}+\color{blue}{(-16)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-16)} + \color{orange}{(\frac{-19}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = ax-16x-\frac{19}{8}a+\frac{19}{8}.16& \text{Uitwerken } \\ & =ax-16x-\frac{19}{8}a+\frac{304}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-16x-\frac{19}{8}a+38 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-17}{13})(x+\frac{19}{8})& =(\color{red}{b}+\color{orange}{\frac{-17}{13}}).(\color{green}{x}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{8}b-\frac{17}{13}x-\frac{17}{13}.\frac{19}{8}& \text{Uitwerken } \\ & =bx+\frac{19}{8}b-\frac{17}{13}x-\frac{323}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{11}{14})(p-\frac{-4}{15})& =(\color{red}{a}+\color{orange}{\frac{11}{14}}).(\color{green}{p}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{11}{14})} . \color{green}{(p)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{15}a+\frac{11}{14}p+\frac{11}{14}.\frac{4}{15}& \text{Uitwerken } \\ & =ap+\frac{4}{15}a+\frac{11}{14}p+\frac{44}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{15}a+\frac{11}{14}p+\frac{22}{105} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{4}-x)(\frac{-7}{16}-q)& =(\color{red}{-x}+\color{orange}{\frac{3}{2}}).(\color{green}{-q}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{16}x-\frac{3}{2}q-\frac{3}{2}.\frac{7}{16}& \text{Uitwerken } \\ & =qx+\frac{7}{16}x-\frac{3}{2}q-\frac{21}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-15}{12})(x-\frac{19}{2})& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{2}a+\frac{5}{4}x-\frac{5}{4}.\frac{19}{2}& \text{Uitwerken } \\ & =ax-\frac{19}{2}a+\frac{5}{4}x-\frac{95}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{18}{18})(b+\frac{-6}{16})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{8}a+1b-1.\frac{3}{8}& \text{Uitwerken } \\ & =ab-\frac{3}{8}a+1b-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{2}+b)(a-\frac{11}{6})& =(\color{red}{b}+\color{orange}{\frac{9}{2}}).(\color{green}{a}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{9}{2})} . \color{green}{(a)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{6}b+\frac{9}{2}a-\frac{9}{2}.\frac{11}{6}& \text{Uitwerken } \\ & =ab-\frac{11}{6}b+\frac{9}{2}a-\frac{99}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{11}{6}b+\frac{9}{2}a-\frac{33}{4} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-06-14 04:30:53