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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{7}+b)(\frac{7}{5}+b)& =(\color{red}{b}+\color{orange}{\frac{16}{7}}).(\color{green}{b}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{16}{7})} . \color{green}{(b)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{7}{5}b+\frac{16}{7}b+\frac{16}{7}.\frac{7}{5}& \text{Uitwerken } \\ & =b^2+(\frac{7}{5}+\frac{16}{7})b+\frac{112}{35} & \text{Neem samen} \\ &=b^2+\frac{129}{35}b+\frac{112}{35} & \text{Maak de som} \\ &=b^2+\frac{129}{35}b+\frac{16}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{10}+q)(\frac{12}{2}-a)& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{-a}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -aq+6q+\frac{4}{5}a-\frac{4}{5}.6& \text{Uitwerken } \\ & =-aq+6q+\frac{4}{5}a-\frac{24}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{3}{6})(\frac{8}{8}+x)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1b-\frac{1}{2}x-\frac{1}{2}.1& \text{Uitwerken } \\ & =bx+1b-\frac{1}{2}x-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{11}-p)(\frac{10}{14}+x)& =(\color{red}{-p}+\color{orange}{\frac{14}{11}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{14}{11})} . \color{green}{(x)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{7}p+\frac{14}{11}x+\frac{14}{11}.\frac{5}{7}& \text{Uitwerken } \\ & =-px-\frac{5}{7}p+\frac{14}{11}x+\frac{70}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{5}{7}p+\frac{14}{11}x+\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{11}-p)(\frac{-1}{7}-x)& =(\color{red}{-p}+\color{orange}{\frac{10}{11}}).(\color{green}{-x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{10}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{7}p-\frac{10}{11}x-\frac{10}{11}.\frac{1}{7}& \text{Uitwerken } \\ & =px+\frac{1}{7}p-\frac{10}{11}x-\frac{10}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{6}+p)(q+\frac{8}{7})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{7}p+1q+1.\frac{8}{7}& \text{Uitwerken } \\ & =pq+\frac{8}{7}p+1q+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{12}-p)(\frac{13}{9}+a)& =(\color{red}{-p}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{9}p+\frac{5}{3}a+\frac{5}{3}.\frac{13}{9}& \text{Uitwerken } \\ & =-ap-\frac{13}{9}p+\frac{5}{3}a+\frac{65}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}((-8)+p)(p-\frac{-20}{12})& =(\color{red}{p}+\color{orange}{(-8)}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(-8)} . \color{green}{(p)} + \color{orange}{(-8)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{3}p-8p-8.\frac{5}{3}& \text{Uitwerken } \\ & =p^2+(\frac{5}{3}+(-8))p-(\frac{-40}{3}) & \text{Neem samen} \\ &=p^2-\frac{19}{3}p-(\frac{-40}{3}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b+\frac{3}{16})(\frac{7}{8}+q)& =(\color{red}{b}+\color{orange}{\frac{3}{16}}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{3}{16})} . \color{green}{(q)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{8}b+\frac{3}{16}q+\frac{3}{16}.\frac{7}{8}& \text{Uitwerken } \\ & =bq+\frac{7}{8}b+\frac{3}{16}q+\frac{21}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{16}{4})(\frac{14}{15}+q)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{14}{15}q-4q-4.\frac{14}{15}& \text{Uitwerken } \\ & =q^2+(\frac{14}{15}+(-4))q-(\frac{-56}{15}) & \text{Neem samen} \\ &=q^2-\frac{46}{15}q-(\frac{-56}{15}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{19}-b)(b+\frac{17}{20})& =(\color{red}{-b}+\color{orange}{\frac{-12}{19}}).(\color{green}{b}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{17}{20}b-\frac{12}{19}b-\frac{12}{19}.\frac{17}{20}& \text{Uitwerken } \\ & =-b^2+((\frac{-17}{20})+(\frac{-12}{19}))b-\frac{204}{380} & \text{Neem samen} \\ &=-b^2-\frac{563}{380}b-\frac{204}{380} & \text{Maak de som} \\ &=-b^2-\frac{563}{380}b-\frac{51}{95} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-19}{9})(x+\frac{8}{6})& =(\color{red}{p}+\color{orange}{\frac{19}{9}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{19}{9})} . \color{green}{(x)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{3}p+\frac{19}{9}x+\frac{19}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =px+\frac{4}{3}p+\frac{19}{9}x+\frac{76}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-01 17:17:52
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