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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{6}{12}+a)(p+\frac{1}{5})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{5}a+\frac{1}{2}p+\frac{1}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =ap+\frac{1}{5}a+\frac{1}{2}p+\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-(-18))(\frac{10}{3}+x)& =(\color{red}{q}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{10}{3}q+18x+18.\frac{10}{3}& \text{Uitwerken } \\ & =qx+\frac{10}{3}q+18x+\frac{180}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{10}{3}q+18x+60 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-12}{18})(\frac{18}{13}-p)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{-p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{18}{13}p-\frac{2}{3}p+\frac{2}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =-p^2+(\frac{18}{13}+(\frac{-2}{3}))p+(\frac{-36}{39}) & \text{Neem samen} \\ &=-p^2+\frac{28}{39}p+(\frac{-36}{39}) & \text{Maak de som} \\ &=-p^2+\frac{28}{39}p+(\frac{-12}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-13}{3})(\frac{-13}{15}-x)& =(\color{red}{p}+\color{orange}{\frac{-13}{3}}).(\color{green}{-x}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{15}p+\frac{13}{3}x+\frac{13}{3}.\frac{13}{15}& \text{Uitwerken } \\ & =-px-\frac{13}{15}p+\frac{13}{3}x+\frac{169}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-16}{17})(b-\frac{-2}{14})& =(\color{red}{a}+\color{orange}{\frac{16}{17}}).(\color{green}{b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{16}{17})} . \color{green}{(b)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{7}a+\frac{16}{17}b+\frac{16}{17}.\frac{1}{7}& \text{Uitwerken } \\ & =ab+\frac{1}{7}a+\frac{16}{17}b+\frac{16}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{18}{18})(\frac{19}{15}+p)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{15}q+1p+1.\frac{19}{15}& \text{Uitwerken } \\ & =pq+\frac{19}{15}q+1p+\frac{19}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{1}{5})(a+\frac{-2}{6})& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{3}a-\frac{1}{5}a+\frac{1}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{3})+(\frac{-1}{5}))a+\frac{1}{15} & \text{Neem samen} \\ &=a^2-\frac{8}{15}a+\frac{1}{15} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{8}{20}+x)(\frac{11}{2}+b)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{2}x+\frac{2}{5}b+\frac{2}{5}.\frac{11}{2}& \text{Uitwerken } \\ & =bx+\frac{11}{2}x+\frac{2}{5}b+\frac{22}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{2}x+\frac{2}{5}b+\frac{11}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-7}{14})(p+\frac{3}{17})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{17}x-\frac{1}{2}p-\frac{1}{2}.\frac{3}{17}& \text{Uitwerken } \\ & =px+\frac{3}{17}x-\frac{1}{2}p-\frac{3}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{14}{20}-q)(12+a)& =(\color{red}{-q}+\color{orange}{\frac{7}{10}}).(\color{green}{a}+\color{blue}{12})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(12)} + \color{orange}{(\frac{7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -aq-12q+\frac{7}{10}a+\frac{7}{10}.12& \text{Uitwerken } \\ & =-aq-12q+\frac{7}{10}a+\frac{84}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-12q+\frac{7}{10}a+\frac{42}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-13}{3})(b-\frac{-1}{12})& =(\color{red}{x}+\color{orange}{\frac{13}{3}}).(\color{green}{b}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{13}{3})} . \color{green}{(b)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{12}x+\frac{13}{3}b+\frac{13}{3}.\frac{1}{12}& \text{Uitwerken } \\ & =bx+\frac{1}{12}x+\frac{13}{3}b+\frac{13}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{6}-b)(\frac{-13}{16}-x)& =(\color{red}{-b}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{16}b-\frac{3}{2}x-\frac{3}{2}.\frac{13}{16}& \text{Uitwerken } \\ & =bx+\frac{13}{16}b-\frac{3}{2}x-\frac{39}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-11 21:32:58
Een site van Busleyden Atheneum Mechelen