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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{3}+b)(\frac{-2}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{16}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{16}{3})} . \color{green}{(x)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}b+\frac{16}{3}x-\frac{16}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}b+\frac{16}{3}x-\frac{16}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{2}b+\frac{16}{3}x-\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-2}{8})(\frac{12}{13}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{12}{13}p+\frac{1}{4}a+\frac{1}{4}.\frac{12}{13}& \text{Uitwerken } \\ & =ap+\frac{12}{13}p+\frac{1}{4}a+\frac{12}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{12}{13}p+\frac{1}{4}a+\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{18}-a)(a+\frac{19}{3})& =(\color{red}{-a}+\color{orange}{\frac{-19}{18}}).(\color{green}{a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{19}{3}a-\frac{19}{18}a-\frac{19}{18}.\frac{19}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-19}{3})+(\frac{-19}{18}))a-\frac{361}{54} & \text{Neem samen} \\ &=-a^2-\frac{133}{18}a-\frac{361}{54} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-10}{3})(\frac{-13}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{10}{3}}).(\color{green}{-b}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{10}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{14}x-\frac{10}{3}b-\frac{10}{3}.\frac{13}{14}& \text{Uitwerken } \\ & =-bx-\frac{13}{14}x-\frac{10}{3}b-\frac{130}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{13}{14}x-\frac{10}{3}b-\frac{65}{21} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{10}{15})(\frac{11}{3}+p)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{3}b-\frac{2}{3}p-\frac{2}{3}.\frac{11}{3}& \text{Uitwerken } \\ & =bp+\frac{11}{3}b-\frac{2}{3}p-\frac{22}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-13}{19})(a+\frac{-1}{3})& =(\color{red}{b}+\color{orange}{\frac{13}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{13}{19})} . \color{green}{(a)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{3}b+\frac{13}{19}a-\frac{13}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =ab-\frac{1}{3}b+\frac{13}{19}a-\frac{13}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{19}{5})(a+\frac{4}{4})& =(\color{red}{x}+\color{orange}{\frac{-19}{5}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1x-\frac{19}{5}a-\frac{19}{5}.1& \text{Uitwerken } \\ & =ax+1x-\frac{19}{5}a-\frac{19}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-6}{11})(\frac{2}{17}-p)& =(\color{red}{b}+\color{orange}{\frac{-6}{11}}).(\color{green}{-p}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{17}b+\frac{6}{11}p-\frac{6}{11}.\frac{2}{17}& \text{Uitwerken } \\ & =-bp+\frac{2}{17}b+\frac{6}{11}p-\frac{12}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{5}{11})(a-\frac{18}{20})& =(\color{red}{p}+\color{orange}{\frac{-5}{11}}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{10}p-\frac{5}{11}a+\frac{5}{11}.\frac{9}{10}& \text{Uitwerken } \\ & =ap-\frac{9}{10}p-\frac{5}{11}a+\frac{45}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{10}p-\frac{5}{11}a+\frac{9}{22} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-16}{9})(\frac{-19}{5}+q)& =(\color{red}{a}+\color{orange}{\frac{16}{9}}).(\color{green}{q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{16}{9})} . \color{green}{(q)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{5}a+\frac{16}{9}q-\frac{16}{9}.\frac{19}{5}& \text{Uitwerken } \\ & =aq-\frac{19}{5}a+\frac{16}{9}q-\frac{304}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{17}{15})(\frac{-16}{6}+p)& =(\color{red}{q}+\color{orange}{\frac{-17}{15}}).(\color{green}{p}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{3}q-\frac{17}{15}p+\frac{17}{15}.\frac{8}{3}& \text{Uitwerken } \\ & =pq-\frac{8}{3}q-\frac{17}{15}p+\frac{136}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{13}{20})(x-\frac{4}{4})& =(\color{red}{p}+\color{orange}{\frac{13}{20}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p+\frac{13}{20}x-\frac{13}{20}.1& \text{Uitwerken } \\ & =px-1p+\frac{13}{20}x-\frac{13}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-24 01:14:24
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