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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-4}{7})(\frac{-4}{16}+b)& =(\color{red}{a}+\color{orange}{\frac{-4}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{4}a-\frac{4}{7}b+\frac{4}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =ab-\frac{1}{4}a-\frac{4}{7}b+\frac{4}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{4}a-\frac{4}{7}b+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{8}+q)(p-\frac{3}{16})& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{16}q+\frac{5}{2}p-\frac{5}{2}.\frac{3}{16}& \text{Uitwerken } \\ & =pq-\frac{3}{16}q+\frac{5}{2}p-\frac{15}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-5}{4})(a-\frac{-6}{9})& =(\color{red}{x}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}x+\frac{5}{4}a+\frac{5}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}x+\frac{5}{4}a+\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}x+\frac{5}{4}a+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}((-18)+p)(p+(-19))& =(\color{red}{p}+\color{orange}{(-18)}).(\color{green}{p}+\color{blue}{(-19)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-19)} + \color{orange}{(-18)} . \color{green}{(p)} + \color{orange}{(-18)} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = pp-19p-18p+18.19& \text{Uitwerken } \\ & =p^2+((-19)+(-18))p+342 & \text{Neem samen} \\ &=p^2-37p+342 & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-14}{8})(a+\frac{-13}{11})& =(\color{red}{a}+\color{orange}{\frac{7}{4}}).(\color{green}{a}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{11}a+\frac{7}{4}a-\frac{7}{4}.\frac{13}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{11})+\frac{7}{4})a-(\frac{-91}{44}) & \text{Neem samen} \\ &=a^2+\frac{25}{44}a-(\frac{-91}{44}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-16}{2})(a-\frac{19}{5})& =(\color{red}{p}+\color{orange}{8}).(\color{green}{a}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(8)} . \color{green}{(a)} + \color{orange}{(8)} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{5}p+8a-8.\frac{19}{5}& \text{Uitwerken } \\ & =ap-\frac{19}{5}p+8a-\frac{152}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{5}-b)(\frac{-2}{6}+p)& =(\color{red}{-b}+\color{orange}{\frac{11}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{3}b+\frac{11}{5}p-\frac{11}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =-bp+\frac{1}{3}b+\frac{11}{5}p-\frac{11}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-15}{20})(\frac{9}{8}+q)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{9}{8}q-\frac{3}{4}q-\frac{3}{4}.\frac{9}{8}& \text{Uitwerken } \\ & =q^2+(\frac{9}{8}+(\frac{-3}{4}))q-(\frac{-27}{32}) & \text{Neem samen} \\ &=q^2+\frac{3}{8}q-(\frac{-27}{32}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{13}{5}-q)(\frac{-12}{16}+a)& =(\color{red}{-q}+\color{orange}{\frac{13}{5}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{13}{5})} . \color{green}{(a)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{4}q+\frac{13}{5}a-\frac{13}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =-aq+\frac{3}{4}q+\frac{13}{5}a-\frac{39}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-14)(p+\frac{-10}{5})& =(\color{red}{b}+\color{orange}{(-14)}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(-14)} . \color{green}{(p)} + \color{orange}{(-14)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bp-2b-14p+14.2& \text{Uitwerken } \\ & =bp-2b-14p+28 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-19}{11})(\frac{20}{19}-p)& =(\color{red}{p}+\color{orange}{\frac{19}{11}}).(\color{green}{-p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{19}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{20}{19}p-\frac{19}{11}p+\frac{19}{11}.\frac{20}{19}& \text{Uitwerken } \\ & =-p^2+(\frac{20}{19}+(\frac{-19}{11}))p+(\frac{-380}{209}) & \text{Neem samen} \\ &=-p^2-\frac{141}{209}p+(\frac{-380}{209}) & \text{Maak de som} \\ &=-p^2-\frac{141}{209}p+(\frac{-20}{11}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{16}+x)(\frac{19}{5}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{19}{5}x+\frac{3}{4}x+\frac{3}{4}.\frac{19}{5}& \text{Uitwerken } \\ & =x^2+(\frac{19}{5}+\frac{3}{4})x+\frac{57}{20} & \text{Neem samen} \\ &=x^2+\frac{91}{20}x+\frac{57}{20} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-03 21:35:49
Een site van Busleyden Atheneum Mechelen