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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{7}{3})(a+\frac{19}{5})& =(\color{red}{a}+\color{orange}{\frac{7}{3}}).(\color{green}{a}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{19}{5}a+\frac{7}{3}a+\frac{7}{3}.\frac{19}{5}& \text{Uitwerken } \\ & =a^2+(\frac{19}{5}+\frac{7}{3})a+\frac{133}{15} & \text{Neem samen} \\ &=a^2+\frac{92}{15}a+\frac{133}{15} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{5}+x)(q+\frac{-9}{12})& =(\color{red}{x}+\color{orange}{\frac{-18}{5}}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{4}x-\frac{18}{5}q+\frac{18}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =qx-\frac{3}{4}x-\frac{18}{5}q+\frac{54}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{4}x-\frac{18}{5}q+\frac{27}{10} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{17}{10})(\frac{5}{3}+a)& =(\color{red}{b}+\color{orange}{\frac{17}{10}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{17}{10})} . \color{green}{(a)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{3}b+\frac{17}{10}a+\frac{17}{10}.\frac{5}{3}& \text{Uitwerken } \\ & =ab+\frac{5}{3}b+\frac{17}{10}a+\frac{85}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{3}b+\frac{17}{10}a+\frac{17}{6} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}((-18)-x)(\frac{13}{9}+x)& =(\color{red}{-x}+\color{orange}{(-18)}).(\color{green}{x}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(-18)} . \color{green}{(x)} + \color{orange}{(-18)} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{13}{9}x-18x-18.\frac{13}{9}& \text{Uitwerken } \\ & =-x^2+((\frac{-13}{9})+(-18))x-\frac{234}{9} & \text{Neem samen} \\ &=-x^2-\frac{175}{9}x-\frac{234}{9} & \text{Maak de som} \\ &=-x^2-\frac{175}{9}x-26 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{3}+b)(b+\frac{-1}{8})& =(\color{red}{b}+\color{orange}{\frac{13}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{13}{3})} . \color{green}{(b)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{8}b+\frac{13}{3}b-\frac{13}{3}.\frac{1}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{8})+\frac{13}{3})b-(\frac{-13}{24}) & \text{Neem samen} \\ &=b^2+\frac{101}{24}b-(\frac{-13}{24}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{16}-q)(x-\frac{-12}{11})& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{12}{11}q+1x+1.\frac{12}{11}& \text{Uitwerken } \\ & =-qx-\frac{12}{11}q+1x+\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{7}-b)(p+\frac{19}{2})& =(\color{red}{-b}+\color{orange}{\frac{-16}{7}}).(\color{green}{p}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{2}b-\frac{16}{7}p-\frac{16}{7}.\frac{19}{2}& \text{Uitwerken } \\ & =-bp-\frac{19}{2}b-\frac{16}{7}p-\frac{304}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{19}{2}b-\frac{16}{7}p-\frac{152}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{11}-p)((-4)-q)& =(\color{red}{-p}+\color{orange}{\frac{1}{11}}).(\color{green}{-q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(-4)} + \color{orange}{(\frac{1}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pq+4p-\frac{1}{11}q-\frac{1}{11}.4& \text{Uitwerken } \\ & =pq+4p-\frac{1}{11}q-\frac{4}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-19}{7})(p+\frac{13}{2})& =(\color{red}{p}+\color{orange}{\frac{19}{7}}).(\color{green}{p}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{19}{7})} . \color{green}{(p)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{2}p+\frac{19}{7}p+\frac{19}{7}.\frac{13}{2}& \text{Uitwerken } \\ & =p^2+(\frac{13}{2}+\frac{19}{7})p+\frac{247}{14} & \text{Neem samen} \\ &=p^2+\frac{129}{14}p+\frac{247}{14} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{8}-a)(p-\frac{-8}{2})& =(\color{red}{-a}+\color{orange}{\frac{9}{8}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(4)} + \color{orange}{(\frac{9}{8})} . \color{green}{(p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -ap-4a+\frac{9}{8}p+\frac{9}{8}.4& \text{Uitwerken } \\ & =-ap-4a+\frac{9}{8}p+\frac{36}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-4a+\frac{9}{8}p+\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{9}{17}+a)(q+\frac{-14}{11})& =(\color{red}{a}+\color{orange}{\frac{9}{17}}).(\color{green}{q}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{9}{17})} . \color{green}{(q)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{14}{11}a+\frac{9}{17}q-\frac{9}{17}.\frac{14}{11}& \text{Uitwerken } \\ & =aq-\frac{14}{11}a+\frac{9}{17}q-\frac{126}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{6}{19})(\frac{-6}{11}+p)& =(\color{red}{q}+\color{orange}{\frac{6}{19}}).(\color{green}{p}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{6}{19})} . \color{green}{(p)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{11}q+\frac{6}{19}p-\frac{6}{19}.\frac{6}{11}& \text{Uitwerken } \\ & =pq-\frac{6}{11}q+\frac{6}{19}p-\frac{36}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-19 22:21:46
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