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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{3}-a)(\frac{-20}{19}+q)& =(\color{red}{-a}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{20}{19}a-5q+5.\frac{20}{19}& \text{Uitwerken } \\ & =-aq+\frac{20}{19}a-5q+\frac{100}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{5}-p)(\frac{2}{17}+q)& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{17}p+3q+3.\frac{2}{17}& \text{Uitwerken } \\ & =-pq-\frac{2}{17}p+3q+\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{8}-b)(p-\frac{9}{8})& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{8}b-2p+2.\frac{9}{8}& \text{Uitwerken } \\ & =-bp+\frac{9}{8}b-2p+\frac{18}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{9}{8}b-2p+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-12}{10})(\frac{-2}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{-6}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{9}q-\frac{6}{5}x+\frac{6}{5}.\frac{1}{9}& \text{Uitwerken } \\ & =qx-\frac{1}{9}q-\frac{6}{5}x+\frac{6}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{9}q-\frac{6}{5}x+\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q+14)(\frac{-2}{17}-p)& =(\color{red}{q}+\color{orange}{14}).(\color{green}{-p}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(14)} . \color{green}{(-p)} + \color{orange}{(14)} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{17}q-14p-14.\frac{2}{17}& \text{Uitwerken } \\ & =-pq-\frac{2}{17}q-14p-\frac{28}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{17}{12})(q-\frac{8}{13})& =(\color{red}{q}+\color{orange}{\frac{17}{12}}).(\color{green}{q}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{17}{12})} . \color{green}{(q)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{8}{13}q+\frac{17}{12}q-\frac{17}{12}.\frac{8}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-8}{13})+\frac{17}{12})q-(\frac{-136}{156}) & \text{Neem samen} \\ &=q^2+\frac{125}{156}q-(\frac{-136}{156}) & \text{Maak de som} \\ &=q^2+\frac{125}{156}q+\frac{34}{39} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-8}{3}+b)(x-\frac{4}{8})& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}b-\frac{8}{3}x+\frac{8}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}b-\frac{8}{3}x+\frac{8}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{2}b-\frac{8}{3}x+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-16}{2})(p+\frac{16}{20})& =(\color{red}{b}+\color{orange}{8}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{5}b+8p+8.\frac{4}{5}& \text{Uitwerken } \\ & =bp+\frac{4}{5}b+8p+\frac{32}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{10}-a)(\frac{-17}{19}-b)& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{19}a+\frac{1}{2}b+\frac{1}{2}.\frac{17}{19}& \text{Uitwerken } \\ & =ab+\frac{17}{19}a+\frac{1}{2}b+\frac{17}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-7}{10})(b+\frac{7}{2})& =(\color{red}{b}+\color{orange}{\frac{7}{10}}).(\color{green}{b}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{7}{2}b+\frac{7}{10}b+\frac{7}{10}.\frac{7}{2}& \text{Uitwerken } \\ & =b^2+(\frac{7}{2}+\frac{7}{10})b+\frac{49}{20} & \text{Neem samen} \\ &=b^2+\frac{42}{10}b+\frac{49}{20} & \text{Maak de som} \\ &=b^2+\frac{21}{5}b+\frac{49}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{20}-q)(b-\frac{-14}{13})& =(\color{red}{-q}+\color{orange}{\frac{-19}{20}}).(\color{green}{b}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{14}{13}q-\frac{19}{20}b-\frac{19}{20}.\frac{14}{13}& \text{Uitwerken } \\ & =-bq-\frac{14}{13}q-\frac{19}{20}b-\frac{266}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{14}{13}q-\frac{19}{20}b-\frac{133}{130} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{2}-x)(x+\frac{12}{15})& =(\color{red}{-x}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{4}{5}x+\frac{7}{2}x+\frac{7}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-x^2+((\frac{-4}{5})+\frac{7}{2})x+(\frac{-28}{10}) & \text{Neem samen} \\ &=-x^2+\frac{27}{10}x+(\frac{-28}{10}) & \text{Maak de som} \\ &=-x^2+\frac{27}{10}x+(\frac{-14}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-24 16:02:47
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