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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(15+p)(p+\frac{1}{19})& =(\color{red}{p}+\color{orange}{15}).(\color{green}{p}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(15)} . \color{green}{(p)} + \color{orange}{(15)} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{19}p+15p+15.\frac{1}{19}& \text{Uitwerken } \\ & =p^2+(\frac{1}{19}+15)p+\frac{15}{19} & \text{Neem samen} \\ &=p^2+\frac{286}{19}p+\frac{15}{19} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{10}+a)(\frac{5}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{2}a+\frac{7}{5}q+\frac{7}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =aq+\frac{5}{2}a+\frac{7}{5}q+\frac{35}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{2}a+\frac{7}{5}q+\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-7}{13})(\frac{13}{9}+q)& =(\color{red}{x}+\color{orange}{\frac{-7}{13}}).(\color{green}{q}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{9}x-\frac{7}{13}q-\frac{7}{13}.\frac{13}{9}& \text{Uitwerken } \\ & =qx+\frac{13}{9}x-\frac{7}{13}q-\frac{91}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{9}x-\frac{7}{13}q-\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{20}-x)(\frac{-5}{13}-a)& =(\color{red}{-x}+\color{orange}{\frac{9}{20}}).(\color{green}{-a}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{9}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{13}x-\frac{9}{20}a-\frac{9}{20}.\frac{5}{13}& \text{Uitwerken } \\ & =ax+\frac{5}{13}x-\frac{9}{20}a-\frac{45}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{5}{13}x-\frac{9}{20}a-\frac{9}{52} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-(-10))(\frac{1}{2}+x)& =(\color{red}{a}+\color{orange}{10}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(10)} . \color{green}{(x)} + \color{orange}{(10)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}a+10x+10.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}a+10x+\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{2}a+10x+5 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-20}{6})(a+\frac{-10}{10})& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aa-1a+\frac{10}{3}a-\frac{10}{3}.1& \text{Uitwerken } \\ & =a^2+((-1)+\frac{10}{3})a-(\frac{-10}{3}) & \text{Neem samen} \\ &=a^2+\frac{7}{3}a-(\frac{-10}{3}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-7}{6})(a+\frac{-6}{9})& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{3}a-\frac{7}{6}a+\frac{7}{6}.\frac{2}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{3})+(\frac{-7}{6}))a+\frac{14}{18} & \text{Neem samen} \\ &=a^2-\frac{11}{6}a+\frac{14}{18} & \text{Maak de som} \\ &=a^2-\frac{11}{6}a+\frac{7}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{9}+b)(x+\frac{-3}{19})& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{19}b-\frac{5}{3}x+\frac{5}{3}.\frac{3}{19}& \text{Uitwerken } \\ & =bx-\frac{3}{19}b-\frac{5}{3}x+\frac{15}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{19}b-\frac{5}{3}x+\frac{5}{19} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{4}-b)(q-\frac{-19}{11})& =(\color{red}{-b}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{19}{11}b+\frac{5}{4}q+\frac{5}{4}.\frac{19}{11}& \text{Uitwerken } \\ & =-bq-\frac{19}{11}b+\frac{5}{4}q+\frac{95}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{4}+q)(q-\frac{14}{19})& =(\color{red}{q}+\color{orange}{\frac{-17}{4}}).(\color{green}{q}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{14}{19}q-\frac{17}{4}q+\frac{17}{4}.\frac{14}{19}& \text{Uitwerken } \\ & =q^2+((\frac{-14}{19})+(\frac{-17}{4}))q+\frac{238}{76} & \text{Neem samen} \\ &=q^2-\frac{379}{76}q+\frac{238}{76} & \text{Maak de som} \\ &=q^2-\frac{379}{76}q+\frac{119}{38} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p+\frac{14}{5})(\frac{9}{9}-x)& =(\color{red}{p}+\color{orange}{\frac{14}{5}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{14}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px+1p-\frac{14}{5}x+\frac{14}{5}.1& \text{Uitwerken } \\ & =-px+1p-\frac{14}{5}x+\frac{14}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{7}{11})(b+\frac{13}{18})& =(\color{red}{a}+\color{orange}{\frac{7}{11}}).(\color{green}{b}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{7}{11})} . \color{green}{(b)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{18}a+\frac{7}{11}b+\frac{7}{11}.\frac{13}{18}& \text{Uitwerken } \\ & =ab+\frac{13}{18}a+\frac{7}{11}b+\frac{91}{198} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-14 13:12:36
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