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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{10}{6})(\frac{-18}{7}+p)& =(\color{red}{q}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{18}{7}q+\frac{5}{3}p-\frac{5}{3}.\frac{18}{7}& \text{Uitwerken } \\ & =pq-\frac{18}{7}q+\frac{5}{3}p-\frac{90}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{18}{7}q+\frac{5}{3}p-\frac{30}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-17}{16})(\frac{13}{2}+a)& =(\color{red}{q}+\color{orange}{\frac{-17}{16}}).(\color{green}{a}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{2}q-\frac{17}{16}a-\frac{17}{16}.\frac{13}{2}& \text{Uitwerken } \\ & =aq+\frac{13}{2}q-\frac{17}{16}a-\frac{221}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{12}-b)(x-\frac{-12}{14})& =(\color{red}{-b}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{6}{7}b+\frac{1}{2}x+\frac{1}{2}.\frac{6}{7}& \text{Uitwerken } \\ & =-bx-\frac{6}{7}b+\frac{1}{2}x+\frac{6}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{6}{7}b+\frac{1}{2}x+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{13}-a)(\frac{13}{12}-p)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{12}a-1p+1.\frac{13}{12}& \text{Uitwerken } \\ & =ap-\frac{13}{12}a-1p+\frac{13}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-16}{10})(p-\frac{3}{19})& =(\color{red}{a}+\color{orange}{\frac{-8}{5}}).(\color{green}{p}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{19}a-\frac{8}{5}p+\frac{8}{5}.\frac{3}{19}& \text{Uitwerken } \\ & =ap-\frac{3}{19}a-\frac{8}{5}p+\frac{24}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{11}-a)(\frac{19}{4}+q)& =(\color{red}{-a}+\color{orange}{\frac{-7}{11}}).(\color{green}{q}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{4}a-\frac{7}{11}q-\frac{7}{11}.\frac{19}{4}& \text{Uitwerken } \\ & =-aq-\frac{19}{4}a-\frac{7}{11}q-\frac{133}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-13}{14})(b-\frac{10}{17})& =(\color{red}{p}+\color{orange}{\frac{-13}{14}}).(\color{green}{b}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{10}{17}p-\frac{13}{14}b+\frac{13}{14}.\frac{10}{17}& \text{Uitwerken } \\ & =bp-\frac{10}{17}p-\frac{13}{14}b+\frac{130}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{10}{17}p-\frac{13}{14}b+\frac{65}{119} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(5-a)(\frac{6}{13}+p)& =(\color{red}{-a}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{6}{13}a+5p+5.\frac{6}{13}& \text{Uitwerken } \\ & =-ap-\frac{6}{13}a+5p+\frac{30}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{19}+x)(\frac{-17}{20}-a)& =(\color{red}{x}+\color{orange}{\frac{-17}{19}}).(\color{green}{-a}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{17}{20}x+\frac{17}{19}a+\frac{17}{19}.\frac{17}{20}& \text{Uitwerken } \\ & =-ax-\frac{17}{20}x+\frac{17}{19}a+\frac{289}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{15}{11})(6-q)& =(\color{red}{a}+\color{orange}{\frac{15}{11}}).(\color{green}{-q}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{15}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -aq+6a-\frac{15}{11}q+\frac{15}{11}.6& \text{Uitwerken } \\ & =-aq+6a-\frac{15}{11}q+\frac{90}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-18}{7})(p-\frac{10}{9})& =(\color{red}{x}+\color{orange}{\frac{18}{7}}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{18}{7})} . \color{green}{(p)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{9}x+\frac{18}{7}p-\frac{18}{7}.\frac{10}{9}& \text{Uitwerken } \\ & =px-\frac{10}{9}x+\frac{18}{7}p-\frac{180}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{9}x+\frac{18}{7}p-\frac{20}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{9}-b)(a-(-8))& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{8})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(8)} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -ab-8b+\frac{4}{3}a+\frac{4}{3}.8& \text{Uitwerken } \\ & =-ab-8b+\frac{4}{3}a+\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-12 05:20:43
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