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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{14}+x)(\frac{-13}{9}+a)& =(\color{red}{x}+\color{orange}{\frac{-19}{14}}).(\color{green}{a}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{9}x-\frac{19}{14}a+\frac{19}{14}.\frac{13}{9}& \text{Uitwerken } \\ & =ax-\frac{13}{9}x-\frac{19}{14}a+\frac{247}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(18+q)(\frac{-15}{12}-a)& =(\color{red}{q}+\color{orange}{18}).(\color{green}{-a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(18)} . \color{green}{(-a)} + \color{orange}{(18)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{4}q-18a-18.\frac{5}{4}& \text{Uitwerken } \\ & =-aq-\frac{5}{4}q-18a-\frac{90}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{4}q-18a-\frac{45}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-14}{12})(x-\frac{-5}{14})& =(\color{red}{x}+\color{orange}{\frac{-7}{6}}).(\color{green}{x}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{5}{14}x-\frac{7}{6}x-\frac{7}{6}.\frac{5}{14}& \text{Uitwerken } \\ & =x^2+(\frac{5}{14}+(\frac{-7}{6}))x-(\frac{-35}{84}) & \text{Neem samen} \\ &=x^2-\frac{34}{42}x-(\frac{-35}{84}) & \text{Maak de som} \\ &=x^2-\frac{17}{21}x+\frac{5}{12} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(\frac{4}{10}+p)(x-\frac{-11}{13})& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{13}p+\frac{2}{5}x+\frac{2}{5}.\frac{11}{13}& \text{Uitwerken } \\ & =px+\frac{11}{13}p+\frac{2}{5}x+\frac{22}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-10}{17})(p+\frac{-13}{16})& =(\color{red}{p}+\color{orange}{\frac{10}{17}}).(\color{green}{p}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{16}p+\frac{10}{17}p-\frac{10}{17}.\frac{13}{16}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{16})+\frac{10}{17})p-(\frac{-130}{272}) & \text{Neem samen} \\ &=p^2-\frac{61}{272}p-(\frac{-130}{272}) & \text{Maak de som} \\ &=p^2-\frac{61}{272}p+\frac{65}{136} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-4}{2})(a-\frac{6}{2})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ap-3p-2a+2.3& \text{Uitwerken } \\ & =ap-3p-2a+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{8}+q)(\frac{15}{3}+b)& =(\color{red}{q}+\color{orange}{\frac{13}{8}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{13}{8})} . \color{green}{(b)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bq+5q+\frac{13}{8}b+\frac{13}{8}.5& \text{Uitwerken } \\ & =bq+5q+\frac{13}{8}b+\frac{65}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-15}{16})(x-\frac{-14}{9})& =(\color{red}{x}+\color{orange}{\frac{-15}{16}}).(\color{green}{x}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{14}{9}x-\frac{15}{16}x-\frac{15}{16}.\frac{14}{9}& \text{Uitwerken } \\ & =x^2+(\frac{14}{9}+(\frac{-15}{16}))x-(\frac{-210}{144}) & \text{Neem samen} \\ &=x^2+\frac{89}{144}x-(\frac{-210}{144}) & \text{Maak de som} \\ &=x^2+\frac{89}{144}x+\frac{35}{24} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-19}{20})(\frac{17}{18}+p)& =(\color{red}{p}+\color{orange}{\frac{19}{20}}).(\color{green}{p}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{19}{20})} . \color{green}{(p)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{18}p+\frac{19}{20}p+\frac{19}{20}.\frac{17}{18}& \text{Uitwerken } \\ & =p^2+(\frac{17}{18}+\frac{19}{20})p+\frac{323}{360} & \text{Neem samen} \\ &=p^2+\frac{341}{180}p+\frac{323}{360} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{13}{7}-b)(\frac{-6}{16}+p)& =(\color{red}{-b}+\color{orange}{\frac{13}{7}}).(\color{green}{p}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{8}b+\frac{13}{7}p-\frac{13}{7}.\frac{3}{8}& \text{Uitwerken } \\ & =-bp+\frac{3}{8}b+\frac{13}{7}p-\frac{39}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{8}-a)(\frac{-16}{10}-q)& =(\color{red}{-a}+\color{orange}{\frac{3}{8}}).(\color{green}{-q}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{3}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{5}a-\frac{3}{8}q-\frac{3}{8}.\frac{8}{5}& \text{Uitwerken } \\ & =aq+\frac{8}{5}a-\frac{3}{8}q-\frac{24}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{8}{5}a-\frac{3}{8}q-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-11}{7})(\frac{19}{20}+a)& =(\color{red}{b}+\color{orange}{\frac{11}{7}}).(\color{green}{a}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{11}{7})} . \color{green}{(a)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{20}b+\frac{11}{7}a+\frac{11}{7}.\frac{19}{20}& \text{Uitwerken } \\ & =ab+\frac{19}{20}b+\frac{11}{7}a+\frac{209}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-15 01:53:04
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