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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{2}{18}-a)(\frac{1}{12}+p)& =(\color{red}{-a}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{12}a+\frac{1}{9}p+\frac{1}{9}.\frac{1}{12}& \text{Uitwerken } \\ & =-ap-\frac{1}{12}a+\frac{1}{9}p+\frac{1}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-9}{9})(x+\frac{-5}{17})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{17}b-1x+1.\frac{5}{17}& \text{Uitwerken } \\ & =bx-\frac{5}{17}b-1x+\frac{5}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{4}{17})(b+\frac{-19}{14})& =(\color{red}{p}+\color{orange}{\frac{4}{17}}).(\color{green}{b}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{4}{17})} . \color{green}{(b)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{14}p+\frac{4}{17}b-\frac{4}{17}.\frac{19}{14}& \text{Uitwerken } \\ & =bp-\frac{19}{14}p+\frac{4}{17}b-\frac{76}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{19}{14}p+\frac{4}{17}b-\frac{38}{119} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-19}{17}+a)(a+\frac{-14}{10})& =(\color{red}{a}+\color{orange}{\frac{-19}{17}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{5}a-\frac{19}{17}a+\frac{19}{17}.\frac{7}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{5})+(\frac{-19}{17}))a+\frac{133}{85} & \text{Neem samen} \\ &=a^2-\frac{214}{85}a+\frac{133}{85} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-20}{3})(\frac{17}{2}-x)& =(\color{red}{q}+\color{orange}{\frac{-20}{3}}).(\color{green}{-x}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{2}q+\frac{20}{3}x-\frac{20}{3}.\frac{17}{2}& \text{Uitwerken } \\ & =-qx+\frac{17}{2}q+\frac{20}{3}x-\frac{340}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{17}{2}q+\frac{20}{3}x-\frac{170}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{19}-x)(p-\frac{2}{6})& =(\color{red}{-x}+\color{orange}{\frac{1}{19}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{19})} . \color{green}{(p)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{3}x+\frac{1}{19}p-\frac{1}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =-px+\frac{1}{3}x+\frac{1}{19}p-\frac{1}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-7}{5}+q)(\frac{-17}{6}+p)& =(\color{red}{q}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{6}q-\frac{7}{5}p+\frac{7}{5}.\frac{17}{6}& \text{Uitwerken } \\ & =pq-\frac{17}{6}q-\frac{7}{5}p+\frac{119}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{16}-q)(\frac{18}{9}+b)& =(\color{red}{-q}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bq-2q-\frac{5}{8}b-\frac{5}{8}.2& \text{Uitwerken } \\ & =-bq-2q-\frac{5}{8}b-\frac{10}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-2q-\frac{5}{8}b-\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{8}{3})(a-\frac{-11}{16})& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{a}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{8}{3})} . \color{green}{(a)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{16}q+\frac{8}{3}a+\frac{8}{3}.\frac{11}{16}& \text{Uitwerken } \\ & =aq+\frac{11}{16}q+\frac{8}{3}a+\frac{88}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{11}{16}q+\frac{8}{3}a+\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-18}{7})(b-\frac{16}{3})& =(\color{red}{b}+\color{orange}{\frac{18}{7}}).(\color{green}{b}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{16}{3}b+\frac{18}{7}b-\frac{18}{7}.\frac{16}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-16}{3})+\frac{18}{7})b-(\frac{-288}{21}) & \text{Neem samen} \\ &=b^2-\frac{58}{21}b-(\frac{-288}{21}) & \text{Maak de som} \\ &=b^2-\frac{58}{21}b+\frac{96}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-7}{3})(a-\frac{19}{19})& =(\color{red}{b}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1b-\frac{7}{3}a+\frac{7}{3}.1& \text{Uitwerken } \\ & =ab-1b-\frac{7}{3}a+\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{3}{3})(\frac{-16}{5}+x)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{5}b+1x-1.\frac{16}{5}& \text{Uitwerken } \\ & =bx-\frac{16}{5}b+1x-\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-30 22:34:54
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