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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{5}{20})(q+\frac{-15}{5})& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = aq-3a+\frac{1}{4}q-\frac{1}{4}.3& \text{Uitwerken } \\ & =aq-3a+\frac{1}{4}q-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}((-10)-q)(\frac{-14}{16}-b)& =(\color{red}{-q}+\color{orange}{(-10)}).(\color{green}{-b}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(-10)} . \color{green}{(-b)} + \color{orange}{(-10)} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{8}q+10b+10.\frac{7}{8}& \text{Uitwerken } \\ & =bq+\frac{7}{8}q+10b+\frac{70}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{8}q+10b+\frac{35}{4} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}((-16)-a)(\frac{-1}{14}-x)& =(\color{red}{-a}+\color{orange}{(-16)}).(\color{green}{-x}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(-16)} . \color{green}{(-x)} + \color{orange}{(-16)} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{14}a+16x+16.\frac{1}{14}& \text{Uitwerken } \\ & =ax+\frac{1}{14}a+16x+\frac{16}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{14}a+16x+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{18}+q)(\frac{-12}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{19}{18}}).(\color{green}{-q}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{19}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{12}{19}q-\frac{19}{18}q-\frac{19}{18}.\frac{12}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-12}{19})+(\frac{-19}{18}))q-\frac{228}{342} & \text{Neem samen} \\ &=-q^2-\frac{577}{342}q-\frac{228}{342} & \text{Maak de som} \\ &=-q^2-\frac{577}{342}q-\frac{2}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{17}-a)(p-\frac{15}{17})& =(\color{red}{-a}+\color{orange}{\frac{-6}{17}}).(\color{green}{p}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{15}{17}a-\frac{6}{17}p+\frac{6}{17}.\frac{15}{17}& \text{Uitwerken } \\ & =-ap+\frac{15}{17}a-\frac{6}{17}p+\frac{90}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{4}{5})(x-\frac{-2}{16})& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{8}a+\frac{4}{5}x+\frac{4}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =ax+\frac{1}{8}a+\frac{4}{5}x+\frac{4}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{8}a+\frac{4}{5}x+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{16}+b)(\frac{-6}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{3}b+\frac{1}{2}p-\frac{1}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =bp-\frac{1}{3}b+\frac{1}{2}p-\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+6)(\frac{-17}{2}+q)& =(\color{red}{a}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{2}a+6q-6.\frac{17}{2}& \text{Uitwerken } \\ & =aq-\frac{17}{2}a+6q-\frac{102}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{17}{2}a+6q-51 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{2}{10})(\frac{-2}{10}+b)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{5}x-\frac{1}{5}b+\frac{1}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =bx-\frac{1}{5}x-\frac{1}{5}b+\frac{1}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{1}{14})(a+8)& =(\color{red}{a}+\color{orange}{\frac{-1}{14}}).(\color{green}{a}+\color{blue}{8})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{-1}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = aa+8a-\frac{1}{14}a-\frac{1}{14}.8& \text{Uitwerken } \\ & =a^2+(8+(\frac{-1}{14}))a-(\frac{-8}{14}) & \text{Neem samen} \\ &=a^2+\frac{111}{14}a-(\frac{-8}{14}) & \text{Maak de som} \\ &=a^2+\frac{111}{14}a+\frac{4}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-10}{6})(p+\frac{4}{14})& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{7}b-\frac{5}{3}p-\frac{5}{3}.\frac{2}{7}& \text{Uitwerken } \\ & =bp+\frac{2}{7}b-\frac{5}{3}p-\frac{10}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{8}-p)(\frac{-2}{20}+b)& =(\color{red}{-p}+\color{orange}{\frac{-15}{8}}).(\color{green}{b}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{10}p-\frac{15}{8}b+\frac{15}{8}.\frac{1}{10}& \text{Uitwerken } \\ & =-bp+\frac{1}{10}p-\frac{15}{8}b+\frac{15}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{10}p-\frac{15}{8}b+\frac{3}{16} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-14 10:17:18
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