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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-18}{17})(\frac{-13}{8}+q)& =(\color{red}{a}+\color{orange}{\frac{18}{17}}).(\color{green}{q}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{18}{17})} . \color{green}{(q)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{8}a+\frac{18}{17}q-\frac{18}{17}.\frac{13}{8}& \text{Uitwerken } \\ & =aq-\frac{13}{8}a+\frac{18}{17}q-\frac{234}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{13}{8}a+\frac{18}{17}q-\frac{117}{68} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-9}{10})(a+\frac{-10}{15})& =(\color{red}{a}+\color{orange}{\frac{-9}{10}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{3}a-\frac{9}{10}a+\frac{9}{10}.\frac{2}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{3})+(\frac{-9}{10}))a+\frac{18}{30} & \text{Neem samen} \\ &=a^2-\frac{47}{30}a+\frac{18}{30} & \text{Maak de som} \\ &=a^2-\frac{47}{30}a+\frac{3}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(b-\frac{14}{16})(\frac{-16}{8}-x)& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{-x}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bx-2b+\frac{7}{8}x+\frac{7}{8}.2& \text{Uitwerken } \\ & =-bx-2b+\frac{7}{8}x+\frac{14}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-2b+\frac{7}{8}x+\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-13)(\frac{12}{13}+q)& =(\color{red}{x}+\color{orange}{(-13)}).(\color{green}{q}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(-13)} . \color{green}{(q)} + \color{orange}{(-13)} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{13}x-13q-13.\frac{12}{13}& \text{Uitwerken } \\ & =qx+\frac{12}{13}x-13q-\frac{156}{13} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{13}x-13q-12 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}((-8)-b)(p-12)& =(\color{red}{-b}+\color{orange}{(-8)}).(\color{green}{p}+\color{blue}{(-12)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-12)} + \color{orange}{(-8)} . \color{green}{(p)} + \color{orange}{(-8)} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = -bp+12b-8p+8.12& \text{Uitwerken } \\ & =-bp+12b-8p+96 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-5}{20})(\frac{-15}{13}+b)& =(\color{red}{p}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{15}{13}p+\frac{1}{4}b-\frac{1}{4}.\frac{15}{13}& \text{Uitwerken } \\ & =bp-\frac{15}{13}p+\frac{1}{4}b-\frac{15}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{19}+a)(p-(-7))& =(\color{red}{a}+\color{orange}{\frac{-3}{19}}).(\color{green}{p}+\color{blue}{7})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(\frac{-3}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = ap+7a-\frac{3}{19}p-\frac{3}{19}.7& \text{Uitwerken } \\ & =ap+7a-\frac{3}{19}p-\frac{21}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{10}{8}+p)(\frac{-8}{13}-p)& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{-p}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{8}{13}p-\frac{5}{4}p-\frac{5}{4}.\frac{8}{13}& \text{Uitwerken } \\ & =-p^2+((\frac{-8}{13})+(\frac{-5}{4}))p-\frac{40}{52} & \text{Neem samen} \\ &=-p^2-\frac{97}{52}p-\frac{40}{52} & \text{Maak de som} \\ &=-p^2-\frac{97}{52}p-\frac{10}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(x-\frac{17}{6})(b-\frac{-17}{18})& =(\color{red}{x}+\color{orange}{\frac{-17}{6}}).(\color{green}{b}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{18}x-\frac{17}{6}b-\frac{17}{6}.\frac{17}{18}& \text{Uitwerken } \\ & =bx+\frac{17}{18}x-\frac{17}{6}b-\frac{289}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{6}{9})(b+\frac{11}{7})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{7}p-\frac{2}{3}b-\frac{2}{3}.\frac{11}{7}& \text{Uitwerken } \\ & =bp+\frac{11}{7}p-\frac{2}{3}b-\frac{22}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{15}{8})(\frac{11}{20}+q)& =(\color{red}{x}+\color{orange}{\frac{15}{8}}).(\color{green}{q}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{15}{8})} . \color{green}{(q)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{20}x+\frac{15}{8}q+\frac{15}{8}.\frac{11}{20}& \text{Uitwerken } \\ & =qx+\frac{11}{20}x+\frac{15}{8}q+\frac{165}{160} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{11}{20}x+\frac{15}{8}q+\frac{33}{32} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{3}-x)(\frac{-5}{19}+x)& =(\color{red}{-x}+\color{orange}{\frac{8}{3}}).(\color{green}{x}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{19}x+\frac{8}{3}x-\frac{8}{3}.\frac{5}{19}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{19}+\frac{8}{3})x-\frac{40}{57} & \text{Neem samen} \\ &=-x^2+\frac{167}{57}x-\frac{40}{57} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-02 04:06:34
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