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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-10}{20}+q)(x-\frac{16}{3})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{3}q-\frac{1}{2}x+\frac{1}{2}.\frac{16}{3}& \text{Uitwerken } \\ & =qx-\frac{16}{3}q-\frac{1}{2}x+\frac{16}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{16}{3}q-\frac{1}{2}x+\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x+\frac{14}{15})(q+\frac{19}{18})& =(\color{red}{x}+\color{orange}{\frac{14}{15}}).(\color{green}{q}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(\frac{14}{15})} . \color{green}{(q)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{18}x+\frac{14}{15}q+\frac{14}{15}.\frac{19}{18}& \text{Uitwerken } \\ & =qx+\frac{19}{18}x+\frac{14}{15}q+\frac{266}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{19}{18}x+\frac{14}{15}q+\frac{133}{135} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{12}-b)(\frac{5}{4}-x)& =(\color{red}{-b}+\color{orange}{\frac{-5}{12}}).(\color{green}{-x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{4}b+\frac{5}{12}x-\frac{5}{12}.\frac{5}{4}& \text{Uitwerken } \\ & =bx-\frac{5}{4}b+\frac{5}{12}x-\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{3}-a)(\frac{-10}{19}-q)& =(\color{red}{-a}+\color{orange}{\frac{16}{3}}).(\color{green}{-q}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{16}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{19}a-\frac{16}{3}q-\frac{16}{3}.\frac{10}{19}& \text{Uitwerken } \\ & =aq+\frac{10}{19}a-\frac{16}{3}q-\frac{160}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-14}{7}+q)(b-\frac{2}{16})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{8}q-2b+2.\frac{1}{8}& \text{Uitwerken } \\ & =bq-\frac{1}{8}q-2b+\frac{2}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{8}q-2b+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-14}{6})(a-\frac{-15}{10})& =(\color{red}{x}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}x-\frac{7}{3}a-\frac{7}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}x-\frac{7}{3}a-\frac{21}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{2}x-\frac{7}{3}a-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{17}-a)(x-\frac{3}{7})& =(\color{red}{-a}+\color{orange}{\frac{5}{17}}).(\color{green}{x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{5}{17})} . \color{green}{(x)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{7}a+\frac{5}{17}x-\frac{5}{17}.\frac{3}{7}& \text{Uitwerken } \\ & =-ax+\frac{3}{7}a+\frac{5}{17}x-\frac{15}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{12}{8})(a+\frac{20}{19})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{20}{19}a+\frac{3}{2}a+\frac{3}{2}.\frac{20}{19}& \text{Uitwerken } \\ & =a^2+(\frac{20}{19}+\frac{3}{2})a+\frac{60}{38} & \text{Neem samen} \\ &=a^2+\frac{97}{38}a+\frac{60}{38} & \text{Maak de som} \\ &=a^2+\frac{97}{38}a+\frac{30}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(x+13)(\frac{14}{14}+b)& =(\color{red}{x}+\color{orange}{13}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(13)} . \color{green}{(b)} + \color{orange}{(13)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+13b+13.1& \text{Uitwerken } \\ & =bx+1x+13b+13 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-11}{15})(\frac{-8}{10}+p)& =(\color{red}{p}+\color{orange}{\frac{-11}{15}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{5}p-\frac{11}{15}p+\frac{11}{15}.\frac{4}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{5})+(\frac{-11}{15}))p+\frac{44}{75} & \text{Neem samen} \\ &=p^2-\frac{23}{15}p+\frac{44}{75} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-14}{18})(a+\frac{19}{20})& =(\color{red}{b}+\color{orange}{\frac{7}{9}}).(\color{green}{a}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{20}b+\frac{7}{9}a+\frac{7}{9}.\frac{19}{20}& \text{Uitwerken } \\ & =ab+\frac{19}{20}b+\frac{7}{9}a+\frac{133}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{9}+b)(\frac{-12}{14}-q)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{7}b-2q-2.\frac{6}{7}& \text{Uitwerken } \\ & =-bq-\frac{6}{7}b-2q-\frac{12}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-01 15:13:20
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