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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+13)((-5)+q)& =(\color{red}{p}+\color{orange}{13}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(13)} . \color{green}{(q)} + \color{orange}{(13)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = pq-5p+13q-13.5& \text{Uitwerken } \\ & =pq-5p+13q-65 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{15}-a)(\frac{13}{19}+q)& =(\color{red}{-a}+\color{orange}{\frac{-2}{15}}).(\color{green}{q}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{19}a-\frac{2}{15}q-\frac{2}{15}.\frac{13}{19}& \text{Uitwerken } \\ & =-aq-\frac{13}{19}a-\frac{2}{15}q-\frac{26}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{11}+b)(p-\frac{-5}{11})& =(\color{red}{b}+\color{orange}{\frac{15}{11}}).(\color{green}{p}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{11}b+\frac{15}{11}p+\frac{15}{11}.\frac{5}{11}& \text{Uitwerken } \\ & =bp+\frac{5}{11}b+\frac{15}{11}p+\frac{75}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{18}-a)(q+\frac{-16}{20})& =(\color{red}{-a}+\color{orange}{\frac{11}{18}}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{11}{18})} . \color{green}{(q)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{5}a+\frac{11}{18}q-\frac{11}{18}.\frac{4}{5}& \text{Uitwerken } \\ & =-aq+\frac{4}{5}a+\frac{11}{18}q-\frac{44}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{4}{5}a+\frac{11}{18}q-\frac{22}{45} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{12}{19})(b-\frac{10}{11})& =(\color{red}{a}+\color{orange}{\frac{12}{19}}).(\color{green}{b}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{12}{19})} . \color{green}{(b)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{10}{11}a+\frac{12}{19}b-\frac{12}{19}.\frac{10}{11}& \text{Uitwerken } \\ & =ab-\frac{10}{11}a+\frac{12}{19}b-\frac{120}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{4}{12})(\frac{-14}{15}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{14}{15}a-\frac{1}{3}b-\frac{1}{3}.\frac{14}{15}& \text{Uitwerken } \\ & =-ab-\frac{14}{15}a-\frac{1}{3}b-\frac{14}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-7}{5}-q)(x-\frac{-3}{5})& =(\color{red}{-q}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{5}q-\frac{7}{5}x-\frac{7}{5}.\frac{3}{5}& \text{Uitwerken } \\ & =-qx-\frac{3}{5}q-\frac{7}{5}x-\frac{21}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-13}{16})(10-x)& =(\color{red}{q}+\color{orange}{\frac{13}{16}}).(\color{green}{-x}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(10)} + \color{orange}{(\frac{13}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -qx+10q-\frac{13}{16}x+\frac{13}{16}.10& \text{Uitwerken } \\ & =-qx+10q-\frac{13}{16}x+\frac{130}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+10q-\frac{13}{16}x+\frac{65}{8} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{11}-a)(\frac{12}{6}+q)& =(\color{red}{-a}+\color{orange}{\frac{-4}{11}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{-4}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2a-\frac{4}{11}q-\frac{4}{11}.2& \text{Uitwerken } \\ & =-aq-2a-\frac{4}{11}q-\frac{8}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{4}+x)(9-x)& =(\color{red}{x}+\color{orange}{4}).(\color{green}{-x}+\color{blue}{9})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(9)} + \color{orange}{(4)} . \color{green}{(-x)} + \color{orange}{(4)} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = -xx+9x-4x+4.9& \text{Uitwerken } \\ & =-x^2+(9+(-4))x+(-36) & \text{Neem samen} \\ &=-x^2+5x+(-36) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-11}{15})(p+\frac{-14}{10})& =(\color{red}{a}+\color{orange}{\frac{11}{15}}).(\color{green}{p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{11}{15})} . \color{green}{(p)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{5}a+\frac{11}{15}p-\frac{11}{15}.\frac{7}{5}& \text{Uitwerken } \\ & =ap-\frac{7}{5}a+\frac{11}{15}p-\frac{77}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{4}+a)(\frac{10}{10}-p)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1a-2p+2.1& \text{Uitwerken } \\ & =-ap+1a-2p+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-06 22:44:14
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