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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-2}{11})(\frac{-4}{8}-x)& =(\color{red}{x}+\color{orange}{\frac{-2}{11}}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{1}{2}x+\frac{2}{11}x+\frac{2}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-1}{2})+\frac{2}{11})x+(\frac{-2}{22}) & \text{Neem samen} \\ &=-x^2-\frac{7}{22}x+(\frac{-2}{22}) & \text{Maak de som} \\ &=-x^2-\frac{7}{22}x+(\frac{-1}{11}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-7}{17})(a+\frac{10}{6})& =(\color{red}{q}+\color{orange}{\frac{7}{17}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{7}{17})} . \color{green}{(a)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{3}q+\frac{7}{17}a+\frac{7}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =aq+\frac{5}{3}q+\frac{7}{17}a+\frac{35}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-13}{11})(\frac{-2}{18}+x)& =(\color{red}{p}+\color{orange}{\frac{13}{11}}).(\color{green}{x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{13}{11})} . \color{green}{(x)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{9}p+\frac{13}{11}x-\frac{13}{11}.\frac{1}{9}& \text{Uitwerken } \\ & =px-\frac{1}{9}p+\frac{13}{11}x-\frac{13}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{13}+b)(a-\frac{14}{7})& =(\color{red}{b}+\color{orange}{\frac{-5}{13}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-5}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b-\frac{5}{13}a+\frac{5}{13}.2& \text{Uitwerken } \\ & =ab-2b-\frac{5}{13}a+\frac{10}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{9}{16})(\frac{17}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{-9}{16}}).(\color{green}{-b}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{17}{12}b+\frac{9}{16}b-\frac{9}{16}.\frac{17}{12}& \text{Uitwerken } \\ & =-b^2+(\frac{17}{12}+\frac{9}{16})b-\frac{153}{192} & \text{Neem samen} \\ &=-b^2+\frac{95}{48}b-\frac{153}{192} & \text{Maak de som} \\ &=-b^2+\frac{95}{48}b-\frac{51}{64} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-12}{19})(a+\frac{14}{14})& =(\color{red}{a}+\color{orange}{\frac{12}{19}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{12}{19})} . \color{green}{(a)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aa+1a+\frac{12}{19}a+\frac{12}{19}.1& \text{Uitwerken } \\ & =a^2+(1+\frac{12}{19})a+\frac{12}{19} & \text{Neem samen} \\ &=a^2+\frac{31}{19}a+\frac{12}{19} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-17}{14})(20-x)& =(\color{red}{x}+\color{orange}{\frac{-17}{14}}).(\color{green}{-x}+\color{blue}{20})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(20)} + \color{orange}{(\frac{-17}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -xx+20x+\frac{17}{14}x-\frac{17}{14}.20& \text{Uitwerken } \\ & =-x^2+(20+\frac{17}{14})x-\frac{340}{14} & \text{Neem samen} \\ &=-x^2+\frac{297}{14}x-\frac{340}{14} & \text{Maak de som} \\ &=-x^2+\frac{297}{14}x-\frac{170}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{5}+p)(\frac{8}{15}-b)& =(\color{red}{p}+\color{orange}{\frac{17}{5}}).(\color{green}{-b}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{17}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{15}p-\frac{17}{5}b+\frac{17}{5}.\frac{8}{15}& \text{Uitwerken } \\ & =-bp+\frac{8}{15}p-\frac{17}{5}b+\frac{136}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{15}+x)(\frac{14}{16}+p)& =(\color{red}{x}+\color{orange}{\frac{7}{15}}).(\color{green}{p}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{8}x+\frac{7}{15}p+\frac{7}{15}.\frac{7}{8}& \text{Uitwerken } \\ & =px+\frac{7}{8}x+\frac{7}{15}p+\frac{49}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{15}+b)(\frac{18}{7}+x)& =(\color{red}{b}+\color{orange}{\frac{16}{15}}).(\color{green}{x}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{16}{15})} . \color{green}{(x)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{18}{7}b+\frac{16}{15}x+\frac{16}{15}.\frac{18}{7}& \text{Uitwerken } \\ & =bx+\frac{18}{7}b+\frac{16}{15}x+\frac{288}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{18}{7}b+\frac{16}{15}x+\frac{96}{35} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{10}{16})(x+\frac{11}{7})& =(\color{red}{a}+\color{orange}{\frac{-5}{8}}).(\color{green}{x}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{7}a-\frac{5}{8}x-\frac{5}{8}.\frac{11}{7}& \text{Uitwerken } \\ & =ax+\frac{11}{7}a-\frac{5}{8}x-\frac{55}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{18}+a)(x+\frac{4}{19})& =(\color{red}{a}+\color{orange}{\frac{5}{18}}).(\color{green}{x}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{5}{18})} . \color{green}{(x)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{19}a+\frac{5}{18}x+\frac{5}{18}.\frac{4}{19}& \text{Uitwerken } \\ & =ax+\frac{4}{19}a+\frac{5}{18}x+\frac{20}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{4}{19}a+\frac{5}{18}x+\frac{10}{171} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-25 13:31:39
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