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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{11}-b)(\frac{19}{6}-a)& =(\color{red}{-b}+\color{orange}{\frac{20}{11}}).(\color{green}{-a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{20}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{6}b-\frac{20}{11}a+\frac{20}{11}.\frac{19}{6}& \text{Uitwerken } \\ & =ab-\frac{19}{6}b-\frac{20}{11}a+\frac{380}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{19}{6}b-\frac{20}{11}a+\frac{190}{33} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{16}{5}+a)(\frac{-19}{19}+b)& =(\color{red}{a}+\color{orange}{\frac{16}{5}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{16}{5})} . \color{green}{(b)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a+\frac{16}{5}b-\frac{16}{5}.1& \text{Uitwerken } \\ & =ab-1a+\frac{16}{5}b-\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{18}-p)(b+\frac{4}{19})& =(\color{red}{-p}+\color{orange}{\frac{-5}{18}}).(\color{green}{b}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{19}p-\frac{5}{18}b-\frac{5}{18}.\frac{4}{19}& \text{Uitwerken } \\ & =-bp-\frac{4}{19}p-\frac{5}{18}b-\frac{20}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{19}p-\frac{5}{18}b-\frac{10}{171} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{9}+q)(x+\frac{-11}{7})& =(\color{red}{q}+\color{orange}{\frac{16}{9}}).(\color{green}{x}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{7}q+\frac{16}{9}x-\frac{16}{9}.\frac{11}{7}& \text{Uitwerken } \\ & =qx-\frac{11}{7}q+\frac{16}{9}x-\frac{176}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-18}{17})(\frac{16}{7}+x)& =(\color{red}{p}+\color{orange}{\frac{18}{17}}).(\color{green}{x}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{18}{17})} . \color{green}{(x)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{16}{7}p+\frac{18}{17}x+\frac{18}{17}.\frac{16}{7}& \text{Uitwerken } \\ & =px+\frac{16}{7}p+\frac{18}{17}x+\frac{288}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{3}{12})(\frac{3}{8}+b)& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{8}p-\frac{1}{4}b-\frac{1}{4}.\frac{3}{8}& \text{Uitwerken } \\ & =bp+\frac{3}{8}p-\frac{1}{4}b-\frac{3}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{8}{7})(q-\frac{-12}{2})& =(\color{red}{a}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = aq+6a+\frac{8}{7}q+\frac{8}{7}.6& \text{Uitwerken } \\ & =aq+6a+\frac{8}{7}q+\frac{48}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{2}+a)(q-\frac{13}{16})& =(\color{red}{a}+\color{orange}{\frac{13}{2}}).(\color{green}{q}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{13}{2})} . \color{green}{(q)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{16}a+\frac{13}{2}q-\frac{13}{2}.\frac{13}{16}& \text{Uitwerken } \\ & =aq-\frac{13}{16}a+\frac{13}{2}q-\frac{169}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{15}-p)(p+\frac{15}{2})& =(\color{red}{-p}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{15}{2}p+\frac{3}{5}p+\frac{3}{5}.\frac{15}{2}& \text{Uitwerken } \\ & =-p^2+((\frac{-15}{2})+\frac{3}{5})p+(\frac{-45}{10}) & \text{Neem samen} \\ &=-p^2-\frac{69}{10}p+(\frac{-45}{10}) & \text{Maak de som} \\ &=-p^2-\frac{69}{10}p+(\frac{-9}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(x-6)(\frac{14}{18}-b)& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{-b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(-6)} . \color{green}{(-b)} + \color{orange}{(-6)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{9}x+6b-6.\frac{7}{9}& \text{Uitwerken } \\ & =-bx+\frac{7}{9}x+6b-\frac{42}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{7}{9}x+6b-\frac{14}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{13}-a)(x+\frac{-4}{19})& =(\color{red}{-a}+\color{orange}{\frac{-19}{13}}).(\color{green}{x}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{19}a-\frac{19}{13}x+\frac{19}{13}.\frac{4}{19}& \text{Uitwerken } \\ & =-ax+\frac{4}{19}a-\frac{19}{13}x+\frac{76}{247} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{4}{19}a-\frac{19}{13}x+\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-5}{14})(p+\frac{18}{12})& =(\color{red}{b}+\color{orange}{\frac{5}{14}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{2}b+\frac{5}{14}p+\frac{5}{14}.\frac{3}{2}& \text{Uitwerken } \\ & =bp+\frac{3}{2}b+\frac{5}{14}p+\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-19 18:40:13
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