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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-18}{5})(\frac{12}{15}-a)& =(\color{red}{p}+\color{orange}{\frac{-18}{5}}).(\color{green}{-a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{5}p+\frac{18}{5}a-\frac{18}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-ap+\frac{4}{5}p+\frac{18}{5}a-\frac{72}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-9}{20})(q+\frac{3}{3})& =(\color{red}{q}+\color{orange}{\frac{-9}{20}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-9}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qq+1q-\frac{9}{20}q-\frac{9}{20}.1& \text{Uitwerken } \\ & =q^2+(1+(\frac{-9}{20}))q-(\frac{-9}{20}) & \text{Neem samen} \\ &=q^2+\frac{11}{20}q-(\frac{-9}{20}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{4}+x)(a-\frac{4}{5})& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{5}x-4a+4.\frac{4}{5}& \text{Uitwerken } \\ & =ax-\frac{4}{5}x-4a+\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-11}{15}+a)(x-\frac{18}{8})& =(\color{red}{a}+\color{orange}{\frac{-11}{15}}).(\color{green}{x}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{4}a-\frac{11}{15}x+\frac{11}{15}.\frac{9}{4}& \text{Uitwerken } \\ & =ax-\frac{9}{4}a-\frac{11}{15}x+\frac{99}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{4}a-\frac{11}{15}x+\frac{33}{20} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{15}{19})(\frac{4}{11}+p)& =(\color{red}{p}+\color{orange}{\frac{-15}{19}}).(\color{green}{p}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{4}{11}p-\frac{15}{19}p-\frac{15}{19}.\frac{4}{11}& \text{Uitwerken } \\ & =p^2+(\frac{4}{11}+(\frac{-15}{19}))p-(\frac{-60}{209}) & \text{Neem samen} \\ &=p^2-\frac{89}{209}p-(\frac{-60}{209}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-8}{4}-b)(\frac{-6}{18}-a)& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{-a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-2)} . \color{green}{(-a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}b+2a+2.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}b+2a+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-15}{2})(x+\frac{-15}{6})& =(\color{red}{q}+\color{orange}{\frac{15}{2}}).(\color{green}{x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{15}{2})} . \color{green}{(x)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{2}q+\frac{15}{2}x-\frac{15}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =qx-\frac{5}{2}q+\frac{15}{2}x-\frac{75}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{8}{8}+b)(x-\frac{11}{16})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{16}b+1x-1.\frac{11}{16}& \text{Uitwerken } \\ & =bx-\frac{11}{16}b+1x-\frac{11}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{1}{7})(\frac{-19}{11}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{7}}).(\color{green}{-p}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{1}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{11}a-\frac{1}{7}p-\frac{1}{7}.\frac{19}{11}& \text{Uitwerken } \\ & =-ap-\frac{19}{11}a-\frac{1}{7}p-\frac{19}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{6}-a)(\frac{-4}{2}-a)& =(\color{red}{-a}+\color{orange}{\frac{-5}{2}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aa+2a+\frac{5}{2}a+\frac{5}{2}.2& \text{Uitwerken } \\ & =a^2+(2+\frac{5}{2})a+\frac{10}{2} & \text{Neem samen} \\ &=a^2+\frac{9}{2}a+\frac{10}{2} & \text{Maak de som} \\ &=a^2+\frac{9}{2}a+5 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p+\frac{19}{18})(x+13)& =(\color{red}{p}+\color{orange}{\frac{19}{18}}).(\color{green}{x}+\color{blue}{13})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(13)} + \color{orange}{(\frac{19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = px+13p+\frac{19}{18}x+\frac{19}{18}.13& \text{Uitwerken } \\ & =px+13p+\frac{19}{18}x+\frac{247}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{18}+q)(\frac{7}{3}+b)& =(\color{red}{q}+\color{orange}{\frac{-10}{9}}).(\color{green}{b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{3}q-\frac{10}{9}b-\frac{10}{9}.\frac{7}{3}& \text{Uitwerken } \\ & =bq+\frac{7}{3}q-\frac{10}{9}b-\frac{70}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-02 02:38:24
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