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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-20}{15})(\frac{17}{18}+q)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{18}q-\frac{4}{3}q-\frac{4}{3}.\frac{17}{18}& \text{Uitwerken } \\ & =q^2+(\frac{17}{18}+(\frac{-4}{3}))q-(\frac{-68}{54}) & \text{Neem samen} \\ &=q^2-\frac{7}{18}q-(\frac{-68}{54}) & \text{Maak de som} \\ &=q^2-\frac{7}{18}q+\frac{34}{27} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(x-\frac{12}{16})(x+\frac{13}{8})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{x}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{13}{8}x-\frac{3}{4}x-\frac{3}{4}.\frac{13}{8}& \text{Uitwerken } \\ & =x^2+(\frac{13}{8}+(\frac{-3}{4}))x-(\frac{-39}{32}) & \text{Neem samen} \\ &=x^2+\frac{7}{8}x-(\frac{-39}{32}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{17}+b)(\frac{-17}{9}+p)& =(\color{red}{b}+\color{orange}{\frac{5}{17}}).(\color{green}{p}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{9}b+\frac{5}{17}p-\frac{5}{17}.\frac{17}{9}& \text{Uitwerken } \\ & =bp-\frac{17}{9}b+\frac{5}{17}p-\frac{85}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{17}{9}b+\frac{5}{17}p-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-1}{8}+b)(\frac{-3}{7}-b)& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{-b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{7}b+\frac{1}{8}b+\frac{1}{8}.\frac{3}{7}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{7})+\frac{1}{8})b+(\frac{-3}{56}) & \text{Neem samen} \\ &=-b^2-\frac{17}{56}b+(\frac{-3}{56}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{17}-a)(\frac{-9}{10}+p)& =(\color{red}{-a}+\color{orange}{\frac{-1}{17}}).(\color{green}{p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{10}a-\frac{1}{17}p+\frac{1}{17}.\frac{9}{10}& \text{Uitwerken } \\ & =-ap+\frac{9}{10}a-\frac{1}{17}p+\frac{9}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{19}{12})(\frac{-12}{4}+q)& =(\color{red}{p}+\color{orange}{\frac{-19}{12}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-19}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pq-3p-\frac{19}{12}q+\frac{19}{12}.3& \text{Uitwerken } \\ & =pq-3p-\frac{19}{12}q+\frac{57}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-3p-\frac{19}{12}q+\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{16}-x)(x-\frac{-18}{15})& =(\color{red}{-x}+\color{orange}{\frac{-11}{16}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{6}{5}x-\frac{11}{16}x-\frac{11}{16}.\frac{6}{5}& \text{Uitwerken } \\ & =-x^2+((\frac{-6}{5})+(\frac{-11}{16}))x-\frac{66}{80} & \text{Neem samen} \\ &=-x^2-\frac{151}{80}x-\frac{66}{80} & \text{Maak de som} \\ &=-x^2-\frac{151}{80}x-\frac{33}{40} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{9}-b)(x+\frac{-14}{13})& =(\color{red}{-b}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{14}{13}b-\frac{1}{3}x+\frac{1}{3}.\frac{14}{13}& \text{Uitwerken } \\ & =-bx+\frac{14}{13}b-\frac{1}{3}x+\frac{14}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{8}+q)(a-\frac{1}{19})& =(\color{red}{q}+\color{orange}{\frac{11}{8}}).(\color{green}{a}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{11}{8})} . \color{green}{(a)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{19}q+\frac{11}{8}a-\frac{11}{8}.\frac{1}{19}& \text{Uitwerken } \\ & =aq-\frac{1}{19}q+\frac{11}{8}a-\frac{11}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-15}{4})(\frac{16}{7}+b)& =(\color{red}{x}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{7}x-\frac{15}{4}b-\frac{15}{4}.\frac{16}{7}& \text{Uitwerken } \\ & =bx+\frac{16}{7}x-\frac{15}{4}b-\frac{240}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{16}{7}x-\frac{15}{4}b-\frac{60}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{12}+x)(\frac{20}{11}+q)& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{11}x+\frac{4}{3}q+\frac{4}{3}.\frac{20}{11}& \text{Uitwerken } \\ & =qx+\frac{20}{11}x+\frac{4}{3}q+\frac{80}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{3}{12}-a)(x-\frac{15}{17})& =(\color{red}{-a}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{15}{17}a+\frac{1}{4}x-\frac{1}{4}.\frac{15}{17}& \text{Uitwerken } \\ & =-ax+\frac{15}{17}a+\frac{1}{4}x-\frac{15}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-17 16:16:29
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