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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{8}-a)(x+\frac{-1}{19})& =(\color{red}{-a}+\color{orange}{\frac{15}{8}}).(\color{green}{x}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{15}{8})} . \color{green}{(x)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{19}a+\frac{15}{8}x-\frac{15}{8}.\frac{1}{19}& \text{Uitwerken } \\ & =-ax+\frac{1}{19}a+\frac{15}{8}x-\frac{15}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{8}-b)(a+\frac{-5}{3})& =(\color{red}{-b}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{3}b-\frac{7}{4}a+\frac{7}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =-ab+\frac{5}{3}b-\frac{7}{4}a+\frac{35}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{13}{10})(q-\frac{-18}{3})& =(\color{red}{b}+\color{orange}{\frac{-13}{10}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{-13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bq+6b-\frac{13}{10}q-\frac{13}{10}.6& \text{Uitwerken } \\ & =bq+6b-\frac{13}{10}q-\frac{78}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+6b-\frac{13}{10}q-\frac{39}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p+\frac{17}{17})(b+\frac{-13}{8})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{8}p+1b-1.\frac{13}{8}& \text{Uitwerken } \\ & =bp-\frac{13}{8}p+1b-\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{4}{8})(\frac{15}{12}+x)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{4}a-\frac{1}{2}x-\frac{1}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =ax+\frac{5}{4}a-\frac{1}{2}x-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{16}+b)(b-\frac{-11}{13})& =(\color{red}{b}+\color{orange}{\frac{7}{16}}).(\color{green}{b}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{7}{16})} . \color{green}{(b)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{13}b+\frac{7}{16}b+\frac{7}{16}.\frac{11}{13}& \text{Uitwerken } \\ & =b^2+(\frac{11}{13}+\frac{7}{16})b+\frac{77}{208} & \text{Neem samen} \\ &=b^2+\frac{267}{208}b+\frac{77}{208} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(p-\frac{13}{20})(q+\frac{-4}{2})& =(\color{red}{p}+\color{orange}{\frac{-13}{20}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-13}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p-\frac{13}{20}q+\frac{13}{20}.2& \text{Uitwerken } \\ & =pq-2p-\frac{13}{20}q+\frac{26}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-2p-\frac{13}{20}q+\frac{13}{10} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{6}-q)(\frac{1}{8}-a)& =(\color{red}{-q}+\color{orange}{\frac{7}{3}}).(\color{green}{-a}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{8}q-\frac{7}{3}a+\frac{7}{3}.\frac{1}{8}& \text{Uitwerken } \\ & =aq-\frac{1}{8}q-\frac{7}{3}a+\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(18-p)(q+\frac{12}{18})& =(\color{red}{-p}+\color{orange}{18}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(18)} . \color{green}{(q)} + \color{orange}{(18)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{3}p+18q+18.\frac{2}{3}& \text{Uitwerken } \\ & =-pq-\frac{2}{3}p+18q+\frac{36}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{2}{3}p+18q+12 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{5}{14})(x-\frac{19}{20})& =(\color{red}{a}+\color{orange}{\frac{-5}{14}}).(\color{green}{x}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{20}a-\frac{5}{14}x+\frac{5}{14}.\frac{19}{20}& \text{Uitwerken } \\ & =ax-\frac{19}{20}a-\frac{5}{14}x+\frac{95}{280} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{19}{20}a-\frac{5}{14}x+\frac{19}{56} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{15}-p)(a-\frac{1}{13})& =(\color{red}{-p}+\color{orange}{\frac{-14}{15}}).(\color{green}{a}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{13}p-\frac{14}{15}a+\frac{14}{15}.\frac{1}{13}& \text{Uitwerken } \\ & =-ap+\frac{1}{13}p-\frac{14}{15}a+\frac{14}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-8}{15})(q+\frac{-6}{20})& =(\color{red}{p}+\color{orange}{\frac{8}{15}}).(\color{green}{q}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{8}{15})} . \color{green}{(q)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{10}p+\frac{8}{15}q-\frac{8}{15}.\frac{3}{10}& \text{Uitwerken } \\ & =pq-\frac{3}{10}p+\frac{8}{15}q-\frac{24}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{10}p+\frac{8}{15}q-\frac{4}{25} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-15 21:22:09
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