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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{4}-p)(\frac{7}{6}-q)& =(\color{red}{-p}+\color{orange}{\frac{-15}{4}}).(\color{green}{-q}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{6}p+\frac{15}{4}q-\frac{15}{4}.\frac{7}{6}& \text{Uitwerken } \\ & =pq-\frac{7}{6}p+\frac{15}{4}q-\frac{105}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{6}p+\frac{15}{4}q-\frac{35}{8} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{10}-q)(\frac{-14}{10}-p)& =(\color{red}{-q}+\color{orange}{\frac{7}{5}}).(\color{green}{-p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{5}q-\frac{7}{5}p-\frac{7}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =pq+\frac{7}{5}q-\frac{7}{5}p-\frac{49}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{10}{9})(x-\frac{-7}{12})& =(\color{red}{q}+\color{orange}{\frac{10}{9}}).(\color{green}{x}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{10}{9})} . \color{green}{(x)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{12}q+\frac{10}{9}x+\frac{10}{9}.\frac{7}{12}& \text{Uitwerken } \\ & =qx+\frac{7}{12}q+\frac{10}{9}x+\frac{70}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{7}{12}q+\frac{10}{9}x+\frac{35}{54} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{11}+b)(\frac{-19}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{16}{11}}).(\color{green}{p}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{16}{11})} . \color{green}{(p)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{18}b+\frac{16}{11}p-\frac{16}{11}.\frac{19}{18}& \text{Uitwerken } \\ & =bp-\frac{19}{18}b+\frac{16}{11}p-\frac{304}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{19}{18}b+\frac{16}{11}p-\frac{152}{99} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{15}-q)(a+\frac{-12}{18})& =(\color{red}{-q}+\color{orange}{\frac{-4}{15}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{2}{3}q-\frac{4}{15}a+\frac{4}{15}.\frac{2}{3}& \text{Uitwerken } \\ & =-aq+\frac{2}{3}q-\frac{4}{15}a+\frac{8}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{18}{6})(p+\frac{9}{20})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{20}b-3p-3.\frac{9}{20}& \text{Uitwerken } \\ & =bp+\frac{9}{20}b-3p-\frac{27}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-5}{7}+a)(b-\frac{13}{7})& =(\color{red}{a}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{7}a-\frac{5}{7}b+\frac{5}{7}.\frac{13}{7}& \text{Uitwerken } \\ & =ab-\frac{13}{7}a-\frac{5}{7}b+\frac{65}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{5}-a)(\frac{4}{9}-x)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{9}a+1x-1.\frac{4}{9}& \text{Uitwerken } \\ & =ax-\frac{4}{9}a+1x-\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-11}{10})(x+\frac{-11}{17})& =(\color{red}{q}+\color{orange}{\frac{11}{10}}).(\color{green}{x}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{11}{10})} . \color{green}{(x)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{17}q+\frac{11}{10}x-\frac{11}{10}.\frac{11}{17}& \text{Uitwerken } \\ & =qx-\frac{11}{17}q+\frac{11}{10}x-\frac{121}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{17}{15})(\frac{-19}{17}+p)& =(\color{red}{a}+\color{orange}{\frac{-17}{15}}).(\color{green}{p}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{17}a-\frac{17}{15}p+\frac{17}{15}.\frac{19}{17}& \text{Uitwerken } \\ & =ap-\frac{19}{17}a-\frac{17}{15}p+\frac{323}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{17}a-\frac{17}{15}p+\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{16}-x)(a-\frac{17}{20})& =(\color{red}{-x}+\color{orange}{\frac{15}{16}}).(\color{green}{a}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{15}{16})} . \color{green}{(a)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{20}x+\frac{15}{16}a-\frac{15}{16}.\frac{17}{20}& \text{Uitwerken } \\ & =-ax+\frac{17}{20}x+\frac{15}{16}a-\frac{255}{320} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{17}{20}x+\frac{15}{16}a-\frac{51}{64} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{12}{12})(p-\frac{8}{3})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{3}p+1p-1.\frac{8}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{3})+1)p-(\frac{-8}{3}) & \text{Neem samen} \\ &=p^2-\frac{5}{3}p-(\frac{-8}{3}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-30 21:58:24
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