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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{18}+a)((-19)-a)& =(\color{red}{a}+\color{orange}{\frac{13}{18}}).(\color{green}{-a}+\color{blue}{(-19)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-19)} + \color{orange}{(\frac{13}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -aa-19a-\frac{13}{18}a-\frac{13}{18}.19& \text{Uitwerken } \\ & =-a^2+((-19)+(\frac{-13}{18}))a-\frac{247}{18} & \text{Neem samen} \\ &=-a^2-\frac{355}{18}a-\frac{247}{18} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x+\frac{9}{16})(\frac{12}{20}-x)& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{-x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{9}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{5}x-\frac{9}{16}x+\frac{9}{16}.\frac{3}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{5}+(\frac{-9}{16}))x+(\frac{-27}{80}) & \text{Neem samen} \\ &=-x^2+\frac{3}{80}x+(\frac{-27}{80}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b+\frac{3}{8})(a+\frac{-13}{9})& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{a}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{9}b+\frac{3}{8}a-\frac{3}{8}.\frac{13}{9}& \text{Uitwerken } \\ & =ab-\frac{13}{9}b+\frac{3}{8}a-\frac{39}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{9}b+\frac{3}{8}a-\frac{13}{24} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-1}{19})(x+\frac{-2}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{19}}).(\color{green}{x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{5}x+\frac{1}{19}x-\frac{1}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{5})+\frac{1}{19})x-(\frac{-1}{95}) & \text{Neem samen} \\ &=x^2-\frac{14}{95}x-(\frac{-1}{95}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{8}-x)(\frac{13}{5}+b)& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{5}x-1b-1.\frac{13}{5}& \text{Uitwerken } \\ & =-bx-\frac{13}{5}x-1b-\frac{13}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{3}-q)(\frac{-19}{8}-x)& =(\color{red}{-q}+\color{orange}{(-3)}).(\color{green}{-x}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(-3)} . \color{green}{(-x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{8}q+3x+3.\frac{19}{8}& \text{Uitwerken } \\ & =qx+\frac{19}{8}q+3x+\frac{57}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-8}{19}-p)(\frac{17}{7}-a)& =(\color{red}{-p}+\color{orange}{\frac{-8}{19}}).(\color{green}{-a}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{7}p+\frac{8}{19}a-\frac{8}{19}.\frac{17}{7}& \text{Uitwerken } \\ & =ap-\frac{17}{7}p+\frac{8}{19}a-\frac{136}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-8)((-8)+b)& =(\color{red}{p}+\color{orange}{(-8)}).(\color{green}{b}+\color{blue}{(-8)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-8)} + \color{orange}{(-8)} . \color{green}{(b)} + \color{orange}{(-8)} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = bp-8p-8b+8.8& \text{Uitwerken } \\ & =bp-8p-8b+64 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{15}{16}+p)(b-\frac{-12}{7})& =(\color{red}{p}+\color{orange}{\frac{15}{16}}).(\color{green}{b}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{15}{16})} . \color{green}{(b)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{7}p+\frac{15}{16}b+\frac{15}{16}.\frac{12}{7}& \text{Uitwerken } \\ & =bp+\frac{12}{7}p+\frac{15}{16}b+\frac{180}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{12}{7}p+\frac{15}{16}b+\frac{45}{28} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{13}-q)(\frac{-5}{5}-b)& =(\color{red}{-q}+\color{orange}{\frac{-17}{13}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q+\frac{17}{13}b+\frac{17}{13}.1& \text{Uitwerken } \\ & =bq+1q+\frac{17}{13}b+\frac{17}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-14}{10})((-20)-b)& =(\color{red}{b}+\color{orange}{\frac{7}{5}}).(\color{green}{-b}+\color{blue}{(-20)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(-20)} + \color{orange}{(\frac{7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -bb-20b-\frac{7}{5}b-\frac{7}{5}.20& \text{Uitwerken } \\ & =-b^2+((-20)+(\frac{-7}{5}))b-\frac{140}{5} & \text{Neem samen} \\ &=-b^2-\frac{107}{5}b-\frac{140}{5} & \text{Maak de som} \\ &=-b^2-\frac{107}{5}b-28 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(x+\frac{8}{4})(b+\frac{-6}{14})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{7}x+2b-2.\frac{3}{7}& \text{Uitwerken } \\ & =bx-\frac{3}{7}x+2b-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-15 05:20:36
Een site van Busleyden Atheneum Mechelen