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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{10}-a)(x-\frac{-13}{16})& =(\color{red}{-a}+\color{orange}{\frac{9}{5}}).(\color{green}{x}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{16}a+\frac{9}{5}x+\frac{9}{5}.\frac{13}{16}& \text{Uitwerken } \\ & =-ax-\frac{13}{16}a+\frac{9}{5}x+\frac{117}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{10}+a)(a-\frac{-11}{19})& =(\color{red}{a}+\color{orange}{\frac{11}{10}}).(\color{green}{a}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{11}{10})} . \color{green}{(a)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{19}a+\frac{11}{10}a+\frac{11}{10}.\frac{11}{19}& \text{Uitwerken } \\ & =a^2+(\frac{11}{19}+\frac{11}{10})a+\frac{121}{190} & \text{Neem samen} \\ &=a^2+\frac{319}{190}a+\frac{121}{190} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(p-12)(\frac{-11}{11}-q)& =(\color{red}{p}+\color{orange}{(-12)}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(-12)} . \color{green}{(-q)} + \color{orange}{(-12)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1p+12q+12.1& \text{Uitwerken } \\ & =-pq-1p+12q+12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{5}-p)(q-\frac{-6}{14})& =(\color{red}{-p}+\color{orange}{\frac{-18}{5}}).(\color{green}{q}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{7}p-\frac{18}{5}q-\frac{18}{5}.\frac{3}{7}& \text{Uitwerken } \\ & =-pq-\frac{3}{7}p-\frac{18}{5}q-\frac{54}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{18}{11})(\frac{-5}{16}+p)& =(\color{red}{q}+\color{orange}{\frac{18}{11}}).(\color{green}{p}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{18}{11})} . \color{green}{(p)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{16}q+\frac{18}{11}p-\frac{18}{11}.\frac{5}{16}& \text{Uitwerken } \\ & =pq-\frac{5}{16}q+\frac{18}{11}p-\frac{90}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{5}{16}q+\frac{18}{11}p-\frac{45}{88} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{8}-q)(q-\frac{10}{8})& =(\color{red}{-q}+\color{orange}{\frac{-9}{4}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{5}{4}q-\frac{9}{4}q+\frac{9}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =-q^2+(\frac{5}{4}+(\frac{-9}{4}))q+(\frac{-45}{16}) & \text{Neem samen} \\ &=-q^2-\frac{4}{4}q+(\frac{-45}{16}) & \text{Maak de som} \\ &=-q^2-1q+(\frac{-45}{16}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{3}+x)(x-\frac{-5}{8})& =(\color{red}{x}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{5}{8}x+\frac{10}{3}x+\frac{10}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =x^2+(\frac{5}{8}+\frac{10}{3})x+\frac{50}{24} & \text{Neem samen} \\ &=x^2+\frac{95}{24}x+\frac{50}{24} & \text{Maak de som} \\ &=x^2+\frac{95}{24}x+\frac{25}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{10}+x)(b-\frac{15}{17})& =(\color{red}{x}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{15}{17}x+\frac{9}{10}b-\frac{9}{10}.\frac{15}{17}& \text{Uitwerken } \\ & =bx-\frac{15}{17}x+\frac{9}{10}b-\frac{135}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{15}{17}x+\frac{9}{10}b-\frac{27}{34} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{2}{3}+a)(\frac{-17}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{-x}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{17}{15}a-\frac{2}{3}x-\frac{2}{3}.\frac{17}{15}& \text{Uitwerken } \\ & =-ax-\frac{17}{15}a-\frac{2}{3}x-\frac{34}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-15}{4})(\frac{1}{19}-b)& =(\color{red}{a}+\color{orange}{\frac{15}{4}}).(\color{green}{-b}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{15}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{19}a-\frac{15}{4}b+\frac{15}{4}.\frac{1}{19}& \text{Uitwerken } \\ & =-ab+\frac{1}{19}a-\frac{15}{4}b+\frac{15}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{8}-q)(q+\frac{-4}{5})& =(\color{red}{-q}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{4}{5}q-\frac{1}{2}q+\frac{1}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-q^2+(\frac{4}{5}+(\frac{-1}{2}))q+(\frac{-4}{10}) & \text{Neem samen} \\ &=-q^2+\frac{3}{10}q+(\frac{-4}{10}) & \text{Maak de som} \\ &=-q^2+\frac{3}{10}q+(\frac{-2}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(b-\frac{12}{6})(\frac{9}{13}-x)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-x}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(-2)} . \color{green}{(-x)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{13}b+2x-2.\frac{9}{13}& \text{Uitwerken } \\ & =-bx+\frac{9}{13}b+2x-\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-10 17:24:26
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