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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{2}+b)(\frac{-11}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{-17}{2}}).(\color{green}{x}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{4}b-\frac{17}{2}x+\frac{17}{2}.\frac{11}{4}& \text{Uitwerken } \\ & =bx-\frac{11}{4}b-\frac{17}{2}x+\frac{187}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-16}{2}-x)(p+\frac{20}{4})& =(\color{red}{-x}+\color{orange}{(-8)}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(5)} + \color{orange}{(-8)} . \color{green}{(p)} + \color{orange}{(-8)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -px-5x-8p-8.5& \text{Uitwerken } \\ & =-px-5x-8p-40 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-12}{4}+x)(a-\frac{17}{2})& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{2}x-3a+3.\frac{17}{2}& \text{Uitwerken } \\ & =ax-\frac{17}{2}x-3a+\frac{51}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{3}{15})(q+\frac{2}{2})& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p+\frac{1}{5}q+\frac{1}{5}.1& \text{Uitwerken } \\ & =pq+1p+\frac{1}{5}q+\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-19}{2})(x+\frac{-3}{15})& =(\color{red}{q}+\color{orange}{\frac{19}{2}}).(\color{green}{x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{19}{2})} . \color{green}{(x)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{5}q+\frac{19}{2}x-\frac{19}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =qx-\frac{1}{5}q+\frac{19}{2}x-\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-5}{19})(\frac{19}{11}+p)& =(\color{red}{p}+\color{orange}{\frac{-5}{19}}).(\color{green}{p}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{19}{11}p-\frac{5}{19}p-\frac{5}{19}.\frac{19}{11}& \text{Uitwerken } \\ & =p^2+(\frac{19}{11}+(\frac{-5}{19}))p-(\frac{-95}{209}) & \text{Neem samen} \\ &=p^2+\frac{306}{209}p-(\frac{-95}{209}) & \text{Maak de som} \\ &=p^2+\frac{306}{209}p+\frac{5}{11} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{15}+x)(p-\frac{-14}{18})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{9}x-1p-1.\frac{7}{9}& \text{Uitwerken } \\ & =px+\frac{7}{9}x-1p-\frac{7}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{15}-b)(\frac{12}{17}+q)& =(\color{red}{-b}+\color{orange}{\frac{13}{15}}).(\color{green}{q}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{12}{17}b+\frac{13}{15}q+\frac{13}{15}.\frac{12}{17}& \text{Uitwerken } \\ & =-bq-\frac{12}{17}b+\frac{13}{15}q+\frac{156}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{12}{17}b+\frac{13}{15}q+\frac{52}{85} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-18}{19}-a)(\frac{13}{16}+q)& =(\color{red}{-a}+\color{orange}{\frac{-18}{19}}).(\color{green}{q}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{16}a-\frac{18}{19}q-\frac{18}{19}.\frac{13}{16}& \text{Uitwerken } \\ & =-aq-\frac{13}{16}a-\frac{18}{19}q-\frac{234}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{13}{16}a-\frac{18}{19}q-\frac{117}{152} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{16}{20})(\frac{16}{3}+a)& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{3}q-\frac{4}{5}a-\frac{4}{5}.\frac{16}{3}& \text{Uitwerken } \\ & =aq+\frac{16}{3}q-\frac{4}{5}a-\frac{64}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{20}-a)(q+\frac{-20}{17})& =(\color{red}{-a}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{20}{17}a+\frac{1}{5}q-\frac{1}{5}.\frac{20}{17}& \text{Uitwerken } \\ & =-aq+\frac{20}{17}a+\frac{1}{5}q-\frac{20}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{20}{17}a+\frac{1}{5}q-\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{15}{3})(p-\frac{6}{17})& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{6}{17}p-5p+5.\frac{6}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-6}{17})+(-5))p+\frac{30}{17} & \text{Neem samen} \\ &=p^2-\frac{91}{17}p+\frac{30}{17} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-12 21:13:35
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