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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-13}{8})(b+\frac{-14}{3})& =(\color{red}{a}+\color{orange}{\frac{-13}{8}}).(\color{green}{b}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{14}{3}a-\frac{13}{8}b+\frac{13}{8}.\frac{14}{3}& \text{Uitwerken } \\ & =ab-\frac{14}{3}a-\frac{13}{8}b+\frac{182}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{14}{3}a-\frac{13}{8}b+\frac{91}{12} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{2}{8})(b+\frac{-11}{11})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1q-\frac{1}{4}b+\frac{1}{4}.1& \text{Uitwerken } \\ & =bq-1q-\frac{1}{4}b+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{1}{17})(q+\frac{-14}{5})& =(\color{red}{x}+\color{orange}{\frac{1}{17}}).(\color{green}{q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{1}{17})} . \color{green}{(q)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{5}x+\frac{1}{17}q-\frac{1}{17}.\frac{14}{5}& \text{Uitwerken } \\ & =qx-\frac{14}{5}x+\frac{1}{17}q-\frac{14}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{13}{13})(b+\frac{20}{17})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{20}{17}a-1b-1.\frac{20}{17}& \text{Uitwerken } \\ & =ab+\frac{20}{17}a-1b-\frac{20}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{19}-b)(x-\frac{-19}{20})& =(\color{red}{-b}+\color{orange}{\frac{4}{19}}).(\color{green}{x}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{4}{19})} . \color{green}{(x)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{20}b+\frac{4}{19}x+\frac{4}{19}.\frac{19}{20}& \text{Uitwerken } \\ & =-bx-\frac{19}{20}b+\frac{4}{19}x+\frac{76}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{19}{20}b+\frac{4}{19}x+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{14}{6})(12-a)& =(\color{red}{q}+\color{orange}{\frac{7}{3}}).(\color{green}{-a}+\color{blue}{12})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(12)} + \color{orange}{(\frac{7}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -aq+12q-\frac{7}{3}a+\frac{7}{3}.12& \text{Uitwerken } \\ & =-aq+12q-\frac{7}{3}a+\frac{84}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+12q-\frac{7}{3}a+28 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{13}{6})(p+(-19))& =(\color{red}{p}+\color{orange}{\frac{-13}{6}}).(\color{green}{p}+\color{blue}{(-19)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-19)} + \color{orange}{(\frac{-13}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = pp-19p-\frac{13}{6}p+\frac{13}{6}.19& \text{Uitwerken } \\ & =p^2+((-19)+(\frac{-13}{6}))p+\frac{247}{6} & \text{Neem samen} \\ &=p^2-\frac{127}{6}p+\frac{247}{6} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q+(-9))(\frac{-12}{9}-a)& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{-a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-9)} . \color{green}{(-a)} + \color{orange}{(-9)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{4}{3}q+9a+9.\frac{4}{3}& \text{Uitwerken } \\ & =-aq-\frac{4}{3}q+9a+\frac{36}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{4}{3}q+9a+12 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-2}{8})(q-\frac{17}{19})& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{19}a+\frac{1}{4}q-\frac{1}{4}.\frac{17}{19}& \text{Uitwerken } \\ & =aq-\frac{17}{19}a+\frac{1}{4}q-\frac{17}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{18}-q)(\frac{12}{17}-b)& =(\color{red}{-q}+\color{orange}{\frac{5}{18}}).(\color{green}{-b}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{5}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{12}{17}q-\frac{5}{18}b+\frac{5}{18}.\frac{12}{17}& \text{Uitwerken } \\ & =bq-\frac{12}{17}q-\frac{5}{18}b+\frac{60}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{12}{17}q-\frac{5}{18}b+\frac{10}{51} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-15}{6}+p)(p-\frac{15}{2})& =(\color{red}{p}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{15}{2}p-\frac{5}{2}p+\frac{5}{2}.\frac{15}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-15}{2})+(\frac{-5}{2}))p+\frac{75}{4} & \text{Neem samen} \\ &=p^2-\frac{20}{2}p+\frac{75}{4} & \text{Maak de som} \\ &=p^2-10p+\frac{75}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-9}{6})(\frac{-4}{6}-q)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{3}b+\frac{3}{2}q+\frac{3}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-bq-\frac{2}{3}b+\frac{3}{2}q+\frac{6}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{2}{3}b+\frac{3}{2}q+1 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-19 07:46:25