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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+16)(b-\frac{-9}{12})& =(\color{red}{a}+\color{orange}{16}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(16)} . \color{green}{(b)} + \color{orange}{(16)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{4}a+16b+16.\frac{3}{4}& \text{Uitwerken } \\ & =ab+\frac{3}{4}a+16b+\frac{48}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{4}a+16b+12 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{19}-p)(\frac{-17}{3}-p)& =(\color{red}{-p}+\color{orange}{\frac{-10}{19}}).(\color{green}{-p}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{3}p+\frac{10}{19}p+\frac{10}{19}.\frac{17}{3}& \text{Uitwerken } \\ & =p^2+(\frac{17}{3}+\frac{10}{19})p+\frac{170}{57} & \text{Neem samen} \\ &=p^2+\frac{353}{57}p+\frac{170}{57} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}((-16)-a)(a+\frac{-5}{12})& =(\color{red}{-a}+\color{orange}{(-16)}).(\color{green}{a}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(-16)} . \color{green}{(a)} + \color{orange}{(-16)} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{5}{12}a-16a+16.\frac{5}{12}& \text{Uitwerken } \\ & =-a^2+(\frac{5}{12}+(-16))a+(\frac{-80}{12}) & \text{Neem samen} \\ &=-a^2-\frac{187}{12}a+(\frac{-80}{12}) & \text{Maak de som} \\ &=-a^2-\frac{187}{12}a+(\frac{-20}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{5}-p)(\frac{10}{16}+b)& =(\color{red}{-p}+\color{orange}{\frac{-9}{5}}).(\color{green}{b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{8}p-\frac{9}{5}b-\frac{9}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =-bp-\frac{5}{8}p-\frac{9}{5}b-\frac{45}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{5}{8}p-\frac{9}{5}b-\frac{9}{8} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{14}{2})(p+\frac{3}{8})& =(\color{red}{p}+\color{orange}{7}).(\color{green}{p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(7)} . \color{green}{(p)} + \color{orange}{(7)} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{3}{8}p+7p+7.\frac{3}{8}& \text{Uitwerken } \\ & =p^2+(\frac{3}{8}+7)p+\frac{21}{8} & \text{Neem samen} \\ &=p^2+\frac{59}{8}p+\frac{21}{8} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-16}{6})(\frac{17}{9}-q)& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{-q}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{17}{9}a-\frac{8}{3}q+\frac{8}{3}.\frac{17}{9}& \text{Uitwerken } \\ & =-aq+\frac{17}{9}a-\frac{8}{3}q+\frac{136}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}((-6)-q)(\frac{-19}{11}-p)& =(\color{red}{-q}+\color{orange}{(-6)}).(\color{green}{-p}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(-6)} . \color{green}{(-p)} + \color{orange}{(-6)} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{11}q+6p+6.\frac{19}{11}& \text{Uitwerken } \\ & =pq+\frac{19}{11}q+6p+\frac{114}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-16}{13})(\frac{16}{19}+p)& =(\color{red}{q}+\color{orange}{\frac{-16}{13}}).(\color{green}{p}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{19}q-\frac{16}{13}p-\frac{16}{13}.\frac{16}{19}& \text{Uitwerken } \\ & =pq+\frac{16}{19}q-\frac{16}{13}p-\frac{256}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{20}-a)(a-\frac{-20}{19})& =(\color{red}{-a}+\color{orange}{\frac{3}{10}}).(\color{green}{a}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{20}{19}a+\frac{3}{10}a+\frac{3}{10}.\frac{20}{19}& \text{Uitwerken } \\ & =-a^2+((\frac{-20}{19})+\frac{3}{10})a+(\frac{-60}{190}) & \text{Neem samen} \\ &=-a^2-\frac{143}{190}a+(\frac{-60}{190}) & \text{Maak de som} \\ &=-a^2-\frac{143}{190}a+(\frac{-6}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(b+\frac{11}{15})(q-\frac{14}{6})& =(\color{red}{b}+\color{orange}{\frac{11}{15}}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{11}{15})} . \color{green}{(q)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{3}b+\frac{11}{15}q-\frac{11}{15}.\frac{7}{3}& \text{Uitwerken } \\ & =bq-\frac{7}{3}b+\frac{11}{15}q-\frac{77}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{9}{20})(x+\frac{-16}{19})& =(\color{red}{q}+\color{orange}{\frac{9}{20}}).(\color{green}{x}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{9}{20})} . \color{green}{(x)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{19}q+\frac{9}{20}x-\frac{9}{20}.\frac{16}{19}& \text{Uitwerken } \\ & =qx-\frac{16}{19}q+\frac{9}{20}x-\frac{144}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{16}{19}q+\frac{9}{20}x-\frac{36}{95} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{13}-b)(\frac{10}{14}-p)& =(\color{red}{-b}+\color{orange}{\frac{-10}{13}}).(\color{green}{-p}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{7}b+\frac{10}{13}p-\frac{10}{13}.\frac{5}{7}& \text{Uitwerken } \\ & =bp-\frac{5}{7}b+\frac{10}{13}p-\frac{50}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-25 08:02:05
Een site van Busleyden Atheneum Mechelen