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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{14}{13})(\frac{8}{3}-x)& =(\color{red}{q}+\color{orange}{\frac{14}{13}}).(\color{green}{-x}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{14}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{8}{3}q-\frac{14}{13}x+\frac{14}{13}.\frac{8}{3}& \text{Uitwerken } \\ & =-qx+\frac{8}{3}q-\frac{14}{13}x+\frac{112}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{5}+a)(a-\frac{15}{14})& =(\color{red}{a}+\color{orange}{\frac{-17}{5}}).(\color{green}{a}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{15}{14}a-\frac{17}{5}a+\frac{17}{5}.\frac{15}{14}& \text{Uitwerken } \\ & =a^2+((\frac{-15}{14})+(\frac{-17}{5}))a+\frac{255}{70} & \text{Neem samen} \\ &=a^2-\frac{313}{70}a+\frac{255}{70} & \text{Maak de som} \\ &=a^2-\frac{313}{70}a+\frac{51}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{16}-b)(b-\frac{7}{8})& =(\color{red}{-b}+\color{orange}{\frac{5}{16}}).(\color{green}{b}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{5}{16})} . \color{green}{(b)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{7}{8}b+\frac{5}{16}b-\frac{5}{16}.\frac{7}{8}& \text{Uitwerken } \\ & =-b^2+(\frac{7}{8}+\frac{5}{16})b-\frac{35}{128} & \text{Neem samen} \\ &=-b^2+\frac{19}{16}b-\frac{35}{128} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x+\frac{11}{14})(b+\frac{9}{18})& =(\color{red}{x}+\color{orange}{\frac{11}{14}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{11}{14})} . \color{green}{(b)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x+\frac{11}{14}b+\frac{11}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x+\frac{11}{14}b+\frac{11}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{14}-a)(\frac{-17}{7}+b)& =(\color{red}{-a}+\color{orange}{\frac{6}{7}}).(\color{green}{b}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{7}a+\frac{6}{7}b-\frac{6}{7}.\frac{17}{7}& \text{Uitwerken } \\ & =-ab+\frac{17}{7}a+\frac{6}{7}b-\frac{102}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-15}{13}-q)(\frac{-1}{19}-a)& =(\color{red}{-q}+\color{orange}{\frac{-15}{13}}).(\color{green}{-a}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{19}q+\frac{15}{13}a+\frac{15}{13}.\frac{1}{19}& \text{Uitwerken } \\ & =aq+\frac{1}{19}q+\frac{15}{13}a+\frac{15}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{4}{7})(\frac{3}{14}-x)& =(\color{red}{q}+\color{orange}{\frac{4}{7}}).(\color{green}{-x}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{4}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{14}q-\frac{4}{7}x+\frac{4}{7}.\frac{3}{14}& \text{Uitwerken } \\ & =-qx+\frac{3}{14}q-\frac{4}{7}x+\frac{12}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{3}{14}q-\frac{4}{7}x+\frac{6}{49} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{17}{17})(\frac{2}{3}-b)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{3}a-1b+1.\frac{2}{3}& \text{Uitwerken } \\ & =-ab+\frac{2}{3}a-1b+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-19}{13})(x+\frac{-6}{20})& =(\color{red}{x}+\color{orange}{\frac{-19}{13}}).(\color{green}{x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{10}x-\frac{19}{13}x+\frac{19}{13}.\frac{3}{10}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{10})+(\frac{-19}{13}))x+\frac{57}{130} & \text{Neem samen} \\ &=x^2-\frac{229}{130}x+\frac{57}{130} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-13}{17})(b+\frac{-11}{3})& =(\color{red}{p}+\color{orange}{\frac{13}{17}}).(\color{green}{b}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{13}{17})} . \color{green}{(b)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{3}p+\frac{13}{17}b-\frac{13}{17}.\frac{11}{3}& \text{Uitwerken } \\ & =bp-\frac{11}{3}p+\frac{13}{17}b-\frac{143}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{2}+q)(\frac{2}{18}+a)& =(\color{red}{q}+\color{orange}{\frac{-13}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{9}q-\frac{13}{2}a-\frac{13}{2}.\frac{1}{9}& \text{Uitwerken } \\ & =aq+\frac{1}{9}q-\frac{13}{2}a-\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{6}{16})(b-\frac{-14}{12})& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{6}a-\frac{3}{8}b-\frac{3}{8}.\frac{7}{6}& \text{Uitwerken } \\ & =ab+\frac{7}{6}a-\frac{3}{8}b-\frac{21}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{7}{6}a-\frac{3}{8}b-\frac{7}{16} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-15 06:03:35
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