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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{13}{16})(q+\frac{20}{13})& =(\color{red}{a}+\color{orange}{\frac{13}{16}}).(\color{green}{q}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{13}{16})} . \color{green}{(q)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{13}a+\frac{13}{16}q+\frac{13}{16}.\frac{20}{13}& \text{Uitwerken } \\ & =aq+\frac{20}{13}a+\frac{13}{16}q+\frac{260}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{20}{13}a+\frac{13}{16}q+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-5}{2}+a)(b+\frac{18}{13})& =(\color{red}{a}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{18}{13}a-\frac{5}{2}b-\frac{5}{2}.\frac{18}{13}& \text{Uitwerken } \\ & =ab+\frac{18}{13}a-\frac{5}{2}b-\frac{90}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{18}{13}a-\frac{5}{2}b-\frac{45}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{15}{9})(p-\frac{-12}{12})& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x+\frac{5}{3}p+\frac{5}{3}.1& \text{Uitwerken } \\ & =px+1x+\frac{5}{3}p+\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-8}{3})(q-\frac{-6}{7})& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{7}a+\frac{8}{3}q+\frac{8}{3}.\frac{6}{7}& \text{Uitwerken } \\ & =aq+\frac{6}{7}a+\frac{8}{3}q+\frac{48}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{6}{7}a+\frac{8}{3}q+\frac{16}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-9)(a-\frac{2}{5})& =(\color{red}{b}+\color{orange}{(-9)}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(-9)} . \color{green}{(a)} + \color{orange}{(-9)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{5}b-9a+9.\frac{2}{5}& \text{Uitwerken } \\ & =ab-\frac{2}{5}b-9a+\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{8}{10})(a+\frac{-15}{2})& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{a}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{2}p+\frac{4}{5}a-\frac{4}{5}.\frac{15}{2}& \text{Uitwerken } \\ & =ap-\frac{15}{2}p+\frac{4}{5}a-\frac{60}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{15}{2}p+\frac{4}{5}a-6 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{4}{16})(b+(-7))& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-7)} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bx-7x-\frac{1}{4}b+\frac{1}{4}.7& \text{Uitwerken } \\ & =bx-7x-\frac{1}{4}b+\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{17}+x)(a-\frac{11}{8})& =(\color{red}{x}+\color{orange}{\frac{-12}{17}}).(\color{green}{a}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{8}x-\frac{12}{17}a+\frac{12}{17}.\frac{11}{8}& \text{Uitwerken } \\ & =ax-\frac{11}{8}x-\frac{12}{17}a+\frac{132}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{11}{8}x-\frac{12}{17}a+\frac{33}{34} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-14}{9})(a+\frac{-1}{10})& =(\color{red}{p}+\color{orange}{\frac{-14}{9}}).(\color{green}{a}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{10}p-\frac{14}{9}a+\frac{14}{9}.\frac{1}{10}& \text{Uitwerken } \\ & =ap-\frac{1}{10}p-\frac{14}{9}a+\frac{14}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{10}p-\frac{14}{9}a+\frac{7}{45} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{15}{8})(a-\frac{-7}{15})& =(\color{red}{a}+\color{orange}{\frac{15}{8}}).(\color{green}{a}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{15}{8})} . \color{green}{(a)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{15}a+\frac{15}{8}a+\frac{15}{8}.\frac{7}{15}& \text{Uitwerken } \\ & =a^2+(\frac{7}{15}+\frac{15}{8})a+\frac{105}{120} & \text{Neem samen} \\ &=a^2+\frac{281}{120}a+\frac{105}{120} & \text{Maak de som} \\ &=a^2+\frac{281}{120}a+\frac{7}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p-\frac{1}{16})(\frac{-14}{18}-p)& =(\color{red}{p}+\color{orange}{\frac{-1}{16}}).(\color{green}{-p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{7}{9}p+\frac{1}{16}p+\frac{1}{16}.\frac{7}{9}& \text{Uitwerken } \\ & =-p^2+((\frac{-7}{9})+\frac{1}{16})p+(\frac{-7}{144}) & \text{Neem samen} \\ &=-p^2-\frac{103}{144}p+(\frac{-7}{144}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{13}-q)(a+\frac{15}{15})& =(\color{red}{-q}+\color{orange}{\frac{-19}{13}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1q-\frac{19}{13}a-\frac{19}{13}.1& \text{Uitwerken } \\ & =-aq-1q-\frac{19}{13}a-\frac{19}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-13 16:30:40
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