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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-6}{5})(\frac{6}{7}-b)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{-b}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{6}{7}a+\frac{6}{5}b-\frac{6}{5}.\frac{6}{7}& \text{Uitwerken } \\ & =-ab+\frac{6}{7}a+\frac{6}{5}b-\frac{36}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{4}-b)(p-\frac{-16}{17})& =(\color{red}{-b}+\color{orange}{\frac{-9}{2}}).(\color{green}{p}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{16}{17}b-\frac{9}{2}p-\frac{9}{2}.\frac{16}{17}& \text{Uitwerken } \\ & =-bp-\frac{16}{17}b-\frac{9}{2}p-\frac{144}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{16}{17}b-\frac{9}{2}p-\frac{72}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{16}-x)(p-\frac{-4}{9})& =(\color{red}{-x}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{9}x+\frac{1}{4}p+\frac{1}{4}.\frac{4}{9}& \text{Uitwerken } \\ & =-px-\frac{4}{9}x+\frac{1}{4}p+\frac{4}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{4}{9}x+\frac{1}{4}p+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-3)(p-\frac{-15}{4})& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{15}{4}x-3p-3.\frac{15}{4}& \text{Uitwerken } \\ & =px+\frac{15}{4}x-3p-\frac{45}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{18}+a)(x-\frac{-18}{17})& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{x}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{18}{17}a-\frac{1}{6}x-\frac{1}{6}.\frac{18}{17}& \text{Uitwerken } \\ & =ax+\frac{18}{17}a-\frac{1}{6}x-\frac{18}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{18}{17}a-\frac{1}{6}x-\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{19}{20})(a+\frac{-14}{13})& =(\color{red}{q}+\color{orange}{\frac{-19}{20}}).(\color{green}{a}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{14}{13}q-\frac{19}{20}a+\frac{19}{20}.\frac{14}{13}& \text{Uitwerken } \\ & =aq-\frac{14}{13}q-\frac{19}{20}a+\frac{266}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{14}{13}q-\frac{19}{20}a+\frac{133}{130} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-18}{8})(a+\frac{-20}{19})& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{20}{19}a+\frac{9}{4}a-\frac{9}{4}.\frac{20}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-20}{19})+\frac{9}{4})a-(\frac{-180}{76}) & \text{Neem samen} \\ &=a^2+\frac{91}{76}a-(\frac{-180}{76}) & \text{Maak de som} \\ &=a^2+\frac{91}{76}a+\frac{45}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(b-\frac{11}{15})(\frac{9}{10}+b)& =(\color{red}{b}+\color{orange}{\frac{-11}{15}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{10}b-\frac{11}{15}b-\frac{11}{15}.\frac{9}{10}& \text{Uitwerken } \\ & =b^2+(\frac{9}{10}+(\frac{-11}{15}))b-(\frac{-99}{150}) & \text{Neem samen} \\ &=b^2+\frac{5}{30}b-(\frac{-99}{150}) & \text{Maak de som} \\ &=b^2+\frac{1}{6}b+\frac{33}{50} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-10}{15})(\frac{-20}{11}+q)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{20}{11}x-\frac{2}{3}q+\frac{2}{3}.\frac{20}{11}& \text{Uitwerken } \\ & =qx-\frac{20}{11}x-\frac{2}{3}q+\frac{40}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{4}{15}+x)(p-\frac{-18}{12})& =(\color{red}{x}+\color{orange}{\frac{4}{15}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{4}{15})} . \color{green}{(p)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{2}x+\frac{4}{15}p+\frac{4}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =px+\frac{3}{2}x+\frac{4}{15}p+\frac{12}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{2}x+\frac{4}{15}p+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{15}+b)(\frac{10}{20}+a)& =(\color{red}{b}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}b-\frac{3}{5}a-\frac{3}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}b-\frac{3}{5}a-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{13}-a)(a+\frac{3}{2})& =(\color{red}{-a}+\color{orange}{\frac{-14}{13}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{2}a-\frac{14}{13}a-\frac{14}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{2})+(\frac{-14}{13}))a-\frac{42}{26} & \text{Neem samen} \\ &=-a^2-\frac{67}{26}a-\frac{42}{26} & \text{Maak de som} \\ &=-a^2-\frac{67}{26}a-\frac{21}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-06 04:38:18
Een site van Busleyden Atheneum Mechelen