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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{17}{14})(a-\frac{-15}{18})& =(\color{red}{x}+\color{orange}{\frac{17}{14}}).(\color{green}{a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{6}x+\frac{17}{14}a+\frac{17}{14}.\frac{5}{6}& \text{Uitwerken } \\ & =ax+\frac{5}{6}x+\frac{17}{14}a+\frac{85}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{5}+b)(p+(-7))& =(\color{red}{b}+\color{orange}{\frac{-8}{5}}).(\color{green}{p}+\color{blue}{(-7)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-7)} + \color{orange}{(\frac{-8}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bp-7b-\frac{8}{5}p+\frac{8}{5}.7& \text{Uitwerken } \\ & =bp-7b-\frac{8}{5}p+\frac{56}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{15}{12})(\frac{20}{15}+x)& =(\color{red}{b}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{3}b-\frac{5}{4}x-\frac{5}{4}.\frac{4}{3}& \text{Uitwerken } \\ & =bx+\frac{4}{3}b-\frac{5}{4}x-\frac{20}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{4}{3}b-\frac{5}{4}x-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{15}{2})(\frac{14}{6}+a)& =(\color{red}{a}+\color{orange}{\frac{-15}{2}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{3}a-\frac{15}{2}a-\frac{15}{2}.\frac{7}{3}& \text{Uitwerken } \\ & =a^2+(\frac{7}{3}+(\frac{-15}{2}))a-(\frac{-105}{6}) & \text{Neem samen} \\ &=a^2-\frac{31}{6}a-(\frac{-105}{6}) & \text{Maak de som} \\ &=a^2-\frac{31}{6}a+\frac{35}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{18}-x)(\frac{-10}{19}-q)& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{10}{19}x-\frac{1}{2}q-\frac{1}{2}.\frac{10}{19}& \text{Uitwerken } \\ & =qx+\frac{10}{19}x-\frac{1}{2}q-\frac{10}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{10}{19}x-\frac{1}{2}q-\frac{5}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-16}{11})(p+\frac{-15}{8})& =(\color{red}{p}+\color{orange}{\frac{-16}{11}}).(\color{green}{p}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{15}{8}p-\frac{16}{11}p+\frac{16}{11}.\frac{15}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-15}{8})+(\frac{-16}{11}))p+\frac{240}{88} & \text{Neem samen} \\ &=p^2-\frac{293}{88}p+\frac{240}{88} & \text{Maak de som} \\ &=p^2-\frac{293}{88}p+\frac{30}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{2}-q)(\frac{-11}{8}+b)& =(\color{red}{-q}+\color{orange}{\frac{15}{2}}).(\color{green}{b}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{15}{2})} . \color{green}{(b)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{11}{8}q+\frac{15}{2}b-\frac{15}{2}.\frac{11}{8}& \text{Uitwerken } \\ & =-bq+\frac{11}{8}q+\frac{15}{2}b-\frac{165}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-5}{7})(a+\frac{15}{19})& =(\color{red}{p}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{15}{19}p-\frac{5}{7}a-\frac{5}{7}.\frac{15}{19}& \text{Uitwerken } \\ & =ap+\frac{15}{19}p-\frac{5}{7}a-\frac{75}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-13}{5})(x-\frac{-7}{20})& =(\color{red}{p}+\color{orange}{\frac{-13}{5}}).(\color{green}{x}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{20}p-\frac{13}{5}x-\frac{13}{5}.\frac{7}{20}& \text{Uitwerken } \\ & =px+\frac{7}{20}p-\frac{13}{5}x-\frac{91}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-11}{19})(b-\frac{9}{19})& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{b}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{11}{19})} . \color{green}{(b)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{19}x+\frac{11}{19}b-\frac{11}{19}.\frac{9}{19}& \text{Uitwerken } \\ & =bx-\frac{9}{19}x+\frac{11}{19}b-\frac{99}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-10}{14}-q)(\frac{9}{11}+x)& =(\color{red}{-q}+\color{orange}{\frac{-5}{7}}).(\color{green}{x}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{9}{11}q-\frac{5}{7}x-\frac{5}{7}.\frac{9}{11}& \text{Uitwerken } \\ & =-qx-\frac{9}{11}q-\frac{5}{7}x-\frac{45}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{3}{18}-p)(p-\frac{19}{13})& =(\color{red}{-p}+\color{orange}{\frac{1}{6}}).(\color{green}{p}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{19}{13}p+\frac{1}{6}p-\frac{1}{6}.\frac{19}{13}& \text{Uitwerken } \\ & =-p^2+(\frac{19}{13}+\frac{1}{6})p-\frac{19}{78} & \text{Neem samen} \\ &=-p^2+\frac{127}{78}p-\frac{19}{78} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-07-15 22:07:56
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