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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{20}-q)(\frac{-14}{13}+a)& =(\color{red}{-q}+\color{orange}{\frac{-17}{20}}).(\color{green}{a}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{14}{13}q-\frac{17}{20}a+\frac{17}{20}.\frac{14}{13}& \text{Uitwerken } \\ & =-aq+\frac{14}{13}q-\frac{17}{20}a+\frac{238}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{14}{13}q-\frac{17}{20}a+\frac{119}{130} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-8}{5})(\frac{-10}{5}+a)& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aq-2q-\frac{8}{5}a+\frac{8}{5}.2& \text{Uitwerken } \\ & =aq-2q-\frac{8}{5}a+\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{9}-a)(a-\frac{-15}{8})& =(\color{red}{-a}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{15}{8}a+\frac{2}{3}a+\frac{2}{3}.\frac{15}{8}& \text{Uitwerken } \\ & =-a^2+((\frac{-15}{8})+\frac{2}{3})a+(\frac{-30}{24}) & \text{Neem samen} \\ &=-a^2-\frac{29}{24}a+(\frac{-30}{24}) & \text{Maak de som} \\ &=-a^2-\frac{29}{24}a+(\frac{-5}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{20}-x)(\frac{-9}{4}-q)& =(\color{red}{-x}+\color{orange}{\frac{-3}{5}}).(\color{green}{-q}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{4}x+\frac{3}{5}q+\frac{3}{5}.\frac{9}{4}& \text{Uitwerken } \\ & =qx+\frac{9}{4}x+\frac{3}{5}q+\frac{27}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{2}+q)(q-\frac{16}{2})& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{q}+\color{blue}{(-8)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-8)} + \color{orange}{(-8)} . \color{green}{(q)} + \color{orange}{(-8)} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = qq-8q-8q+8.8& \text{Uitwerken } \\ & =q^2+((-8)+(-8))q+64 & \text{Neem samen} \\ &=q^2-16q+64 & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b-\frac{9}{7})(\frac{4}{12}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{7}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{3}b-\frac{9}{7}b-\frac{9}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+(\frac{1}{3}+(\frac{-9}{7}))b-(\frac{-9}{21}) & \text{Neem samen} \\ &=b^2-\frac{20}{21}b-(\frac{-9}{21}) & \text{Maak de som} \\ &=b^2-\frac{20}{21}b+\frac{3}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(a-\frac{6}{16})(b+\frac{2}{15})& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{15}a-\frac{3}{8}b-\frac{3}{8}.\frac{2}{15}& \text{Uitwerken } \\ & =ab+\frac{2}{15}a-\frac{3}{8}b-\frac{6}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{15}a-\frac{3}{8}b-\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{8}+b)(\frac{19}{11}-x)& =(\color{red}{b}+\color{orange}{\frac{15}{8}}).(\color{green}{-x}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{15}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{19}{11}b-\frac{15}{8}x+\frac{15}{8}.\frac{19}{11}& \text{Uitwerken } \\ & =-bx+\frac{19}{11}b-\frac{15}{8}x+\frac{285}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-(-20))(\frac{18}{5}+a)& =(\color{red}{q}+\color{orange}{20}).(\color{green}{a}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(20)} . \color{green}{(a)} + \color{orange}{(20)} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{18}{5}q+20a+20.\frac{18}{5}& \text{Uitwerken } \\ & =aq+\frac{18}{5}q+20a+\frac{360}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{18}{5}q+20a+72 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{19}-p)(\frac{19}{6}+x)& =(\color{red}{-p}+\color{orange}{\frac{18}{19}}).(\color{green}{x}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{18}{19})} . \color{green}{(x)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{6}p+\frac{18}{19}x+\frac{18}{19}.\frac{19}{6}& \text{Uitwerken } \\ & =-px-\frac{19}{6}p+\frac{18}{19}x+\frac{342}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{19}{6}p+\frac{18}{19}x+3 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p-\frac{11}{18})(x+\frac{-19}{18})& =(\color{red}{p}+\color{orange}{\frac{-11}{18}}).(\color{green}{x}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{18}p-\frac{11}{18}x+\frac{11}{18}.\frac{19}{18}& \text{Uitwerken } \\ & =px-\frac{19}{18}p-\frac{11}{18}x+\frac{209}{324} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-6}{9}+p)(\frac{13}{2}+a)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{2}p-\frac{2}{3}a-\frac{2}{3}.\frac{13}{2}& \text{Uitwerken } \\ & =ap+\frac{13}{2}p-\frac{2}{3}a-\frac{26}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{13}{2}p-\frac{2}{3}a-\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-02 12:02:55
Een site van Busleyden Atheneum Mechelen