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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-17}{12})(p-\frac{4}{13})& =(\color{red}{q}+\color{orange}{\frac{-17}{12}}).(\color{green}{p}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{13}q-\frac{17}{12}p+\frac{17}{12}.\frac{4}{13}& \text{Uitwerken } \\ & =pq-\frac{4}{13}q-\frac{17}{12}p+\frac{68}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{13}q-\frac{17}{12}p+\frac{17}{39} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-5}{20})(x+\frac{-20}{16})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{4}x+\frac{1}{4}x-\frac{1}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{4})+\frac{1}{4})x-(\frac{-5}{16}) & \text{Neem samen} \\ &=x^2-\frac{4}{4}x-(\frac{-5}{16}) & \text{Maak de som} \\ &=x^2-1x+\frac{5}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(b-\frac{13}{19})(\frac{18}{5}-x)& =(\color{red}{b}+\color{orange}{\frac{-13}{19}}).(\color{green}{-x}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{18}{5}b+\frac{13}{19}x-\frac{13}{19}.\frac{18}{5}& \text{Uitwerken } \\ & =-bx+\frac{18}{5}b+\frac{13}{19}x-\frac{234}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}((-6)-q)(b-\frac{-4}{5})& =(\color{red}{-q}+\color{orange}{(-6)}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(-6)} . \color{green}{(b)} + \color{orange}{(-6)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{5}q-6b-6.\frac{4}{5}& \text{Uitwerken } \\ & =-bq-\frac{4}{5}q-6b-\frac{24}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-11}{10}+b)(\frac{-2}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{-11}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{9}b-\frac{11}{10}p+\frac{11}{10}.\frac{1}{9}& \text{Uitwerken } \\ & =bp-\frac{1}{9}b-\frac{11}{10}p+\frac{11}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-3}{3})(a-\frac{-9}{17})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{17}x+1a+1.\frac{9}{17}& \text{Uitwerken } \\ & =ax+\frac{9}{17}x+1a+\frac{9}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{16}{19})(\frac{16}{16}+p)& =(\color{red}{p}+\color{orange}{\frac{-16}{19}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pp+1p-\frac{16}{19}p-\frac{16}{19}.1& \text{Uitwerken } \\ & =p^2+(1+(\frac{-16}{19}))p-(\frac{-16}{19}) & \text{Neem samen} \\ &=p^2+\frac{3}{19}p-(\frac{-16}{19}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{20}-p)(\frac{-13}{15}-a)& =(\color{red}{-p}+\color{orange}{\frac{-3}{20}}).(\color{green}{-a}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{15}p+\frac{3}{20}a+\frac{3}{20}.\frac{13}{15}& \text{Uitwerken } \\ & =ap+\frac{13}{15}p+\frac{3}{20}a+\frac{39}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{13}{15}p+\frac{3}{20}a+\frac{13}{100} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{6}{12})(\frac{-12}{10}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{6}{5}b+\frac{1}{2}q-\frac{1}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =bq-\frac{6}{5}b+\frac{1}{2}q-\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{6}{5}b+\frac{1}{2}q-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{9}{6})(\frac{11}{10}+x)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{10}b-\frac{3}{2}x-\frac{3}{2}.\frac{11}{10}& \text{Uitwerken } \\ & =bx+\frac{11}{10}b-\frac{3}{2}x-\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{6}-a)(x-\frac{19}{7})& =(\color{red}{-a}+\color{orange}{\frac{13}{6}}).(\color{green}{x}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{7}a+\frac{13}{6}x-\frac{13}{6}.\frac{19}{7}& \text{Uitwerken } \\ & =-ax+\frac{19}{7}a+\frac{13}{6}x-\frac{247}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{2}+x)(p+\frac{-11}{12})& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{12}x-5p+5.\frac{11}{12}& \text{Uitwerken } \\ & =px-\frac{11}{12}x-5p+\frac{55}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-24 19:53:40
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