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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-(-10))(a+\frac{-10}{12})& =(\color{red}{b}+\color{orange}{10}).(\color{green}{a}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(10)} . \color{green}{(a)} + \color{orange}{(10)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{6}b+10a-10.\frac{5}{6}& \text{Uitwerken } \\ & =ab-\frac{5}{6}b+10a-\frac{50}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{6}b+10a-\frac{25}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-6}{11})(\frac{-9}{7}+q)& =(\color{red}{p}+\color{orange}{\frac{6}{11}}).(\color{green}{q}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{6}{11})} . \color{green}{(q)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{9}{7}p+\frac{6}{11}q-\frac{6}{11}.\frac{9}{7}& \text{Uitwerken } \\ & =pq-\frac{9}{7}p+\frac{6}{11}q-\frac{54}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{11}{16})(q+\frac{10}{14})& =(\color{red}{q}+\color{orange}{\frac{-11}{16}}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{7}q-\frac{11}{16}q-\frac{11}{16}.\frac{5}{7}& \text{Uitwerken } \\ & =q^2+(\frac{5}{7}+(\frac{-11}{16}))q-(\frac{-55}{112}) & \text{Neem samen} \\ &=q^2+\frac{3}{112}q-(\frac{-55}{112}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-10}{15})(x-\frac{5}{3})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{3}b+\frac{2}{3}x-\frac{2}{3}.\frac{5}{3}& \text{Uitwerken } \\ & =bx-\frac{5}{3}b+\frac{2}{3}x-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{2}{13}+b)(x-\frac{-18}{3})& =(\color{red}{b}+\color{orange}{\frac{2}{13}}).(\color{green}{x}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bx+6b+\frac{2}{13}x+\frac{2}{13}.6& \text{Uitwerken } \\ & =bx+6b+\frac{2}{13}x+\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-17}{3}-a)(a-\frac{-13}{18})& =(\color{red}{-a}+\color{orange}{\frac{-17}{3}}).(\color{green}{a}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{13}{18}a-\frac{17}{3}a-\frac{17}{3}.\frac{13}{18}& \text{Uitwerken } \\ & =-a^2+((\frac{-13}{18})+(\frac{-17}{3}))a-\frac{221}{54} & \text{Neem samen} \\ &=-a^2-\frac{115}{18}a-\frac{221}{54} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b-\frac{8}{4})(\frac{-13}{11}+p)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{11}b-2p+2.\frac{13}{11}& \text{Uitwerken } \\ & =bp-\frac{13}{11}b-2p+\frac{26}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{10}-a)(q+\frac{-1}{19})& =(\color{red}{-a}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{19}a-\frac{3}{5}q+\frac{3}{5}.\frac{1}{19}& \text{Uitwerken } \\ & =-aq+\frac{1}{19}a-\frac{3}{5}q+\frac{3}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-10}{8})(12-a)& =(\color{red}{x}+\color{orange}{\frac{5}{4}}).(\color{green}{-a}+\color{blue}{12})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(12)} + \color{orange}{(\frac{5}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -ax+12x-\frac{5}{4}a+\frac{5}{4}.12& \text{Uitwerken } \\ & =-ax+12x-\frac{5}{4}a+\frac{60}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+12x-\frac{5}{4}a+15 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-10}{15})(\frac{-1}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{-p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{6}p+\frac{2}{3}p+\frac{2}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{6})+\frac{2}{3})p+(\frac{-2}{18}) & \text{Neem samen} \\ &=-p^2+\frac{3}{6}p+(\frac{-2}{18}) & \text{Maak de som} \\ &=-p^2+\frac{1}{2}p+(\frac{-1}{9}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(a-\frac{10}{3})(\frac{-18}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{q}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{17}a-\frac{10}{3}q+\frac{10}{3}.\frac{18}{17}& \text{Uitwerken } \\ & =aq-\frac{18}{17}a-\frac{10}{3}q+\frac{180}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{18}{17}a-\frac{10}{3}q+\frac{60}{17} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{20}+q)(\frac{17}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{-19}{20}}).(\color{green}{-a}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{17}{6}q+\frac{19}{20}a-\frac{19}{20}.\frac{17}{6}& \text{Uitwerken } \\ & =-aq+\frac{17}{6}q+\frac{19}{20}a-\frac{323}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-02 16:12:22
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