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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-6}{6})(x+\frac{-10}{4})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{2}b-1x+1.\frac{5}{2}& \text{Uitwerken } \\ & =bx-\frac{5}{2}b-1x+\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(8+a)(a+\frac{15}{18})& =(\color{red}{a}+\color{orange}{8}).(\color{green}{a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(8)} . \color{green}{(a)} + \color{orange}{(8)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{6}a+8a+8.\frac{5}{6}& \text{Uitwerken } \\ & =a^2+(\frac{5}{6}+8)a+\frac{40}{6} & \text{Neem samen} \\ &=a^2+\frac{53}{6}a+\frac{40}{6} & \text{Maak de som} \\ &=a^2+\frac{53}{6}a+\frac{20}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{3}{2}+p)(b+\frac{2}{15})& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{15}p+\frac{3}{2}b+\frac{3}{2}.\frac{2}{15}& \text{Uitwerken } \\ & =bp+\frac{2}{15}p+\frac{3}{2}b+\frac{6}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{15}p+\frac{3}{2}b+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{4}+a)(p+\frac{20}{15})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}a+3p+3.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}a+3p+\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{3}a+3p+4 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{19}+p)(q-\frac{1}{13})& =(\color{red}{p}+\color{orange}{\frac{-9}{19}}).(\color{green}{q}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{13}p-\frac{9}{19}q+\frac{9}{19}.\frac{1}{13}& \text{Uitwerken } \\ & =pq-\frac{1}{13}p-\frac{9}{19}q+\frac{9}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-19}{18})(q+\frac{1}{7})& =(\color{red}{q}+\color{orange}{\frac{19}{18}}).(\color{green}{q}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{19}{18})} . \color{green}{(q)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{7}q+\frac{19}{18}q+\frac{19}{18}.\frac{1}{7}& \text{Uitwerken } \\ & =q^2+(\frac{1}{7}+\frac{19}{18})q+\frac{19}{126} & \text{Neem samen} \\ &=q^2+\frac{151}{126}q+\frac{19}{126} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{13}-b)(5-b)& =(\color{red}{-b}+\color{orange}{\frac{15}{13}}).(\color{green}{-b}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(5)} + \color{orange}{(\frac{15}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bb-5b-\frac{15}{13}b+\frac{15}{13}.5& \text{Uitwerken } \\ & =b^2+((-5)+(\frac{-15}{13}))b+\frac{75}{13} & \text{Neem samen} \\ &=b^2-\frac{80}{13}b+\frac{75}{13} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-3}{20})(a+\frac{2}{11})& =(\color{red}{a}+\color{orange}{\frac{-3}{20}}).(\color{green}{a}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{11}a-\frac{3}{20}a-\frac{3}{20}.\frac{2}{11}& \text{Uitwerken } \\ & =a^2+(\frac{2}{11}+(\frac{-3}{20}))a-(\frac{-6}{220}) & \text{Neem samen} \\ &=a^2+\frac{7}{220}a-(\frac{-6}{220}) & \text{Maak de som} \\ &=a^2+\frac{7}{220}a+\frac{3}{110} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{10}-a)(p-\frac{-14}{12})& =(\color{red}{-a}+\color{orange}{\frac{-17}{10}}).(\color{green}{p}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{6}a-\frac{17}{10}p-\frac{17}{10}.\frac{7}{6}& \text{Uitwerken } \\ & =-ap-\frac{7}{6}a-\frac{17}{10}p-\frac{119}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{11}-x)(a+\frac{13}{3})& =(\color{red}{-x}+\color{orange}{\frac{16}{11}}).(\color{green}{a}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{16}{11})} . \color{green}{(a)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{3}x+\frac{16}{11}a+\frac{16}{11}.\frac{13}{3}& \text{Uitwerken } \\ & =-ax-\frac{13}{3}x+\frac{16}{11}a+\frac{208}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{12}{12})(a-\frac{-11}{14})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{14}a+1a+1.\frac{11}{14}& \text{Uitwerken } \\ & =a^2+(\frac{11}{14}+1)a+\frac{11}{14} & \text{Neem samen} \\ &=a^2+\frac{25}{14}a+\frac{11}{14} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p-\frac{8}{13})(x-\frac{-18}{6})& =(\color{red}{p}+\color{orange}{\frac{-8}{13}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-8}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = px+3p-\frac{8}{13}x-\frac{8}{13}.3& \text{Uitwerken } \\ & =px+3p-\frac{8}{13}x-\frac{24}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-24 19:46:51
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