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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{17}{9})(p+\frac{9}{19})& =(\color{red}{a}+\color{orange}{\frac{-17}{9}}).(\color{green}{p}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{19}a-\frac{17}{9}p-\frac{17}{9}.\frac{9}{19}& \text{Uitwerken } \\ & =ap+\frac{9}{19}a-\frac{17}{9}p-\frac{153}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{19}a-\frac{17}{9}p-\frac{17}{19} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{14}{2})(4+x)& =(\color{red}{q}+\color{orange}{7}).(\color{green}{x}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(7)} . \color{green}{(x)} + \color{orange}{(7)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = qx+4q+7x+7.4& \text{Uitwerken } \\ & =qx+4q+7x+28 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{13}-p)(\frac{18}{7}-a)& =(\color{red}{-p}+\color{orange}{\frac{-11}{13}}).(\color{green}{-a}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{18}{7}p+\frac{11}{13}a-\frac{11}{13}.\frac{18}{7}& \text{Uitwerken } \\ & =ap-\frac{18}{7}p+\frac{11}{13}a-\frac{198}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{6}{15})(q-\frac{1}{2})& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}b-\frac{2}{5}q+\frac{2}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}b-\frac{2}{5}q+\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{2}b-\frac{2}{5}q+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{4}{20})(b-\frac{15}{6})& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{2}p+\frac{1}{5}b-\frac{1}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =bp-\frac{5}{2}p+\frac{1}{5}b-\frac{5}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{2}p+\frac{1}{5}b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-2}{17})(a+7)& =(\color{red}{b}+\color{orange}{\frac{2}{17}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(7)} + \color{orange}{(\frac{2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = ab+7b+\frac{2}{17}a+\frac{2}{17}.7& \text{Uitwerken } \\ & =ab+7b+\frac{2}{17}a+\frac{14}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-15}{6})(x-\frac{13}{5})& =(\color{red}{p}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{5}p+\frac{5}{2}x-\frac{5}{2}.\frac{13}{5}& \text{Uitwerken } \\ & =px-\frac{13}{5}p+\frac{5}{2}x-\frac{65}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{13}{5}p+\frac{5}{2}x-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{1}{14})((-14)+q)& =(\color{red}{p}+\color{orange}{\frac{1}{14}}).(\color{green}{q}+\color{blue}{(-14)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-14)} + \color{orange}{(\frac{1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = pq-14p+\frac{1}{14}q-\frac{1}{14}.14& \text{Uitwerken } \\ & =pq-14p+\frac{1}{14}q-\frac{14}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-14p+\frac{1}{14}q-1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{17}{18}-b)(x-\frac{7}{8})& =(\color{red}{-b}+\color{orange}{\frac{17}{18}}).(\color{green}{x}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{17}{18})} . \color{green}{(x)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{8}b+\frac{17}{18}x-\frac{17}{18}.\frac{7}{8}& \text{Uitwerken } \\ & =-bx+\frac{7}{8}b+\frac{17}{18}x-\frac{119}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{4}-b)(q+\frac{-12}{14})& =(\color{red}{-b}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{6}{7}b-4q+4.\frac{6}{7}& \text{Uitwerken } \\ & =-bq+\frac{6}{7}b-4q+\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-19}{11})(p-\frac{-11}{4})& =(\color{red}{q}+\color{orange}{\frac{-19}{11}}).(\color{green}{p}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{4}q-\frac{19}{11}p-\frac{19}{11}.\frac{11}{4}& \text{Uitwerken } \\ & =pq+\frac{11}{4}q-\frac{19}{11}p-\frac{209}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{11}{4}q-\frac{19}{11}p-\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}((-4)-b)(\frac{-6}{15}+p)& =(\color{red}{-b}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{5}b-4p+4.\frac{2}{5}& \text{Uitwerken } \\ & =-bp+\frac{2}{5}b-4p+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-09 16:46:17
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