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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-5}{17}-x)(\frac{-3}{3}+a)& =(\color{red}{-x}+\color{orange}{\frac{-5}{17}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-5}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1x-\frac{5}{17}a+\frac{5}{17}.1& \text{Uitwerken } \\ & =-ax+1x-\frac{5}{17}a+\frac{5}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-19}{4})(q+\frac{16}{19})& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{q}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{19}{4})} . \color{green}{(q)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{16}{19}q+\frac{19}{4}q+\frac{19}{4}.\frac{16}{19}& \text{Uitwerken } \\ & =q^2+(\frac{16}{19}+\frac{19}{4})q+\frac{304}{76} & \text{Neem samen} \\ &=q^2+\frac{425}{76}q+\frac{304}{76} & \text{Maak de som} \\ &=q^2+\frac{425}{76}q+4 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{12}+x)(a+\frac{13}{8})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{8}x-\frac{1}{2}a-\frac{1}{2}.\frac{13}{8}& \text{Uitwerken } \\ & =ax+\frac{13}{8}x-\frac{1}{2}a-\frac{13}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-7}{17})(\frac{-16}{13}+b)& =(\color{red}{a}+\color{orange}{\frac{-7}{17}}).(\color{green}{b}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{16}{13}a-\frac{7}{17}b+\frac{7}{17}.\frac{16}{13}& \text{Uitwerken } \\ & =ab-\frac{16}{13}a-\frac{7}{17}b+\frac{112}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{19}{3}+b)(a+\frac{20}{2})& =(\color{red}{b}+\color{orange}{\frac{19}{3}}).(\color{green}{a}+\color{blue}{10})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(10)} + \color{orange}{(\frac{19}{3})} . \color{green}{(a)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = ab+10b+\frac{19}{3}a+\frac{19}{3}.10& \text{Uitwerken } \\ & =ab+10b+\frac{19}{3}a+\frac{190}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{11}+x)(b-\frac{-20}{14})& =(\color{red}{x}+\color{orange}{\frac{-9}{11}}).(\color{green}{b}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{7}x-\frac{9}{11}b-\frac{9}{11}.\frac{10}{7}& \text{Uitwerken } \\ & =bx+\frac{10}{7}x-\frac{9}{11}b-\frac{90}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{15}{16})(a+\frac{11}{4})& =(\color{red}{p}+\color{orange}{\frac{15}{16}}).(\color{green}{a}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{15}{16})} . \color{green}{(a)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{4}p+\frac{15}{16}a+\frac{15}{16}.\frac{11}{4}& \text{Uitwerken } \\ & =ap+\frac{11}{4}p+\frac{15}{16}a+\frac{165}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{7}-q)(q+\frac{6}{20})& =(\color{red}{-q}+\color{orange}{\frac{-12}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-12}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{3}{10}q-\frac{12}{7}q-\frac{12}{7}.\frac{3}{10}& \text{Uitwerken } \\ & =-q^2+((\frac{-3}{10})+(\frac{-12}{7}))q-\frac{36}{70} & \text{Neem samen} \\ &=-q^2-\frac{141}{70}q-\frac{36}{70} & \text{Maak de som} \\ &=-q^2-\frac{141}{70}q-\frac{18}{35} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{9}-p)(b+\frac{-15}{4})& =(\color{red}{-p}+\color{orange}{\frac{-14}{9}}).(\color{green}{b}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{15}{4}p-\frac{14}{9}b+\frac{14}{9}.\frac{15}{4}& \text{Uitwerken } \\ & =-bp+\frac{15}{4}p-\frac{14}{9}b+\frac{210}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{15}{4}p-\frac{14}{9}b+\frac{35}{6} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{14}{16}+a)(p-\frac{9}{18})& =(\color{red}{a}+\color{orange}{\frac{7}{8}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{2}a+\frac{7}{8}p-\frac{7}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =ap-\frac{1}{2}a+\frac{7}{8}p-\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{9}{2})(q+\frac{3}{10})& =(\color{red}{p}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{10}p+\frac{9}{2}q+\frac{9}{2}.\frac{3}{10}& \text{Uitwerken } \\ & =pq+\frac{3}{10}p+\frac{9}{2}q+\frac{27}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{8}{16})(q+\frac{14}{14})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-\frac{1}{2}q-\frac{1}{2}.1& \text{Uitwerken } \\ & =bq+1b-\frac{1}{2}q-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-07 19:05:43
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