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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-5}{9})(\frac{17}{17}-p)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1b+\frac{5}{9}p-\frac{5}{9}.1& \text{Uitwerken } \\ & =-bp+1b+\frac{5}{9}p-\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{9}-a)(p-\frac{-18}{4})& =(\color{red}{-a}+\color{orange}{\frac{19}{9}}).(\color{green}{p}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{19}{9})} . \color{green}{(p)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{2}a+\frac{19}{9}p+\frac{19}{9}.\frac{9}{2}& \text{Uitwerken } \\ & =-ap-\frac{9}{2}a+\frac{19}{9}p+\frac{171}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{9}{2}a+\frac{19}{9}p+\frac{19}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{16}-q)(x-\frac{17}{17})& =(\color{red}{-q}+\color{orange}{\frac{-7}{8}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1q-\frac{7}{8}x+\frac{7}{8}.1& \text{Uitwerken } \\ & =-qx+1q-\frac{7}{8}x+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-2}{13})(\frac{4}{16}-a)& =(\color{red}{a}+\color{orange}{\frac{2}{13}}).(\color{green}{-a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{2}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{4}a-\frac{2}{13}a+\frac{2}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{4}+(\frac{-2}{13}))a+(\frac{-2}{52}) & \text{Neem samen} \\ &=-a^2+\frac{5}{52}a+(\frac{-2}{52}) & \text{Maak de som} \\ &=-a^2+\frac{5}{52}a+(\frac{-1}{26}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-17}{11})(\frac{8}{10}+q)& =(\color{red}{x}+\color{orange}{\frac{17}{11}}).(\color{green}{q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{17}{11})} . \color{green}{(q)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{5}x+\frac{17}{11}q+\frac{17}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =qx+\frac{4}{5}x+\frac{17}{11}q+\frac{68}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{11}{8})(\frac{6}{14}+x)& =(\color{red}{q}+\color{orange}{\frac{-11}{8}}).(\color{green}{x}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{7}q-\frac{11}{8}x-\frac{11}{8}.\frac{3}{7}& \text{Uitwerken } \\ & =qx+\frac{3}{7}q-\frac{11}{8}x-\frac{33}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(9+x)(a-\frac{-20}{10})& =(\color{red}{x}+\color{orange}{9}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(9)} . \color{green}{(a)} + \color{orange}{(9)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2x+9a+9.2& \text{Uitwerken } \\ & =ax+2x+9a+18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-3}{17})(p-\frac{-15}{5})& =(\color{red}{b}+\color{orange}{\frac{-3}{17}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{-3}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp+3b-\frac{3}{17}p-\frac{3}{17}.3& \text{Uitwerken } \\ & =bp+3b-\frac{3}{17}p-\frac{9}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-1}{6})(x-\frac{-13}{3})& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{3}p+\frac{1}{6}x+\frac{1}{6}.\frac{13}{3}& \text{Uitwerken } \\ & =px+\frac{13}{3}p+\frac{1}{6}x+\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{7}{5})(\frac{-19}{14}+q)& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{q}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{14}x-\frac{7}{5}q+\frac{7}{5}.\frac{19}{14}& \text{Uitwerken } \\ & =qx-\frac{19}{14}x-\frac{7}{5}q+\frac{133}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{19}{14}x-\frac{7}{5}q+\frac{19}{10} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-13}{18})(\frac{-4}{15}+p)& =(\color{red}{b}+\color{orange}{\frac{-13}{18}}).(\color{green}{p}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{15}b-\frac{13}{18}p+\frac{13}{18}.\frac{4}{15}& \text{Uitwerken } \\ & =bp-\frac{4}{15}b-\frac{13}{18}p+\frac{52}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{15}b-\frac{13}{18}p+\frac{26}{135} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{6}-a)(\frac{-13}{12}+p)& =(\color{red}{-a}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{12}a-\frac{3}{2}p+\frac{3}{2}.\frac{13}{12}& \text{Uitwerken } \\ & =-ap+\frac{13}{12}a-\frac{3}{2}p+\frac{39}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{13}{12}a-\frac{3}{2}p+\frac{13}{8} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-27 01:51:10
Een site van Busleyden Atheneum Mechelen