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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{14}-q)(a-\frac{12}{6})& =(\color{red}{-q}+\color{orange}{\frac{5}{14}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-2)} + \color{orange}{(\frac{5}{14})} . \color{green}{(a)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq+2q+\frac{5}{14}a-\frac{5}{14}.2& \text{Uitwerken } \\ & =-aq+2q+\frac{5}{14}a-\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+2q+\frac{5}{14}a-\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{15}-p)(b+\frac{9}{15})& =(\color{red}{-p}+\color{orange}{\frac{-6}{5}}).(\color{green}{b}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{5}p-\frac{6}{5}b-\frac{6}{5}.\frac{3}{5}& \text{Uitwerken } \\ & =-bp-\frac{3}{5}p-\frac{6}{5}b-\frac{18}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{6}-a)(\frac{-18}{8}-p)& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{4}a-\frac{1}{3}p-\frac{1}{3}.\frac{9}{4}& \text{Uitwerken } \\ & =ap+\frac{9}{4}a-\frac{1}{3}p-\frac{9}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{4}a-\frac{1}{3}p-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{19}{19})(\frac{10}{17}+q)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{17}a+1q+1.\frac{10}{17}& \text{Uitwerken } \\ & =aq+\frac{10}{17}a+1q+\frac{10}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{4}+a)(\frac{13}{17}+x)& =(\color{red}{a}+\color{orange}{\frac{-9}{4}}).(\color{green}{x}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{17}a-\frac{9}{4}x-\frac{9}{4}.\frac{13}{17}& \text{Uitwerken } \\ & =ax+\frac{13}{17}a-\frac{9}{4}x-\frac{117}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-19}{14})(\frac{12}{20}+q)& =(\color{red}{q}+\color{orange}{\frac{19}{14}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{19}{14})} . \color{green}{(q)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{5}q+\frac{19}{14}q+\frac{19}{14}.\frac{3}{5}& \text{Uitwerken } \\ & =q^2+(\frac{3}{5}+\frac{19}{14})q+\frac{57}{70} & \text{Neem samen} \\ &=q^2+\frac{137}{70}q+\frac{57}{70} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{5}-a)(p-\frac{-15}{11})& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{15}{11}a+2p+2.\frac{15}{11}& \text{Uitwerken } \\ & =-ap-\frac{15}{11}a+2p+\frac{30}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{11}{16})(\frac{2}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{-11}{16}}).(\color{green}{-b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{6}b+\frac{11}{16}b-\frac{11}{16}.\frac{1}{6}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{6}+\frac{11}{16})b-\frac{11}{96} & \text{Neem samen} \\ &=-b^2+\frac{41}{48}b-\frac{11}{96} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-13}{17}-x)(q-8)& =(\color{red}{-x}+\color{orange}{\frac{-13}{17}}).(\color{green}{q}+\color{blue}{(-8)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-8)} + \color{orange}{(\frac{-13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -qx+8x-\frac{13}{17}q+\frac{13}{17}.8& \text{Uitwerken } \\ & =-qx+8x-\frac{13}{17}q+\frac{104}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-6}{17}+x)(\frac{-15}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-6}{17}}).(\color{green}{a}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{2}x-\frac{6}{17}a+\frac{6}{17}.\frac{15}{2}& \text{Uitwerken } \\ & =ax-\frac{15}{2}x-\frac{6}{17}a+\frac{90}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{15}{2}x-\frac{6}{17}a+\frac{45}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{13}{5})(a+\frac{-5}{2})& =(\color{red}{b}+\color{orange}{\frac{13}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{13}{5})} . \color{green}{(a)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{2}b+\frac{13}{5}a-\frac{13}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =ab-\frac{5}{2}b+\frac{13}{5}a-\frac{65}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{2}b+\frac{13}{5}a-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{17}{8})(\frac{-5}{12}+p)& =(\color{red}{b}+\color{orange}{\frac{17}{8}}).(\color{green}{p}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{17}{8})} . \color{green}{(p)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{12}b+\frac{17}{8}p-\frac{17}{8}.\frac{5}{12}& \text{Uitwerken } \\ & =bp-\frac{5}{12}b+\frac{17}{8}p-\frac{85}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-14 13:31:56
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