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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-18}{2})(x-\frac{11}{5})& =(\color{red}{p}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{5}p-9x+9.\frac{11}{5}& \text{Uitwerken } \\ & =px-\frac{11}{5}p-9x+\frac{99}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{14}{17})(q-\frac{-16}{12})& =(\color{red}{b}+\color{orange}{\frac{-14}{17}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{3}b-\frac{14}{17}q-\frac{14}{17}.\frac{4}{3}& \text{Uitwerken } \\ & =bq+\frac{4}{3}b-\frac{14}{17}q-\frac{56}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}((-3)+q)(\frac{3}{18}-q)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{-q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(-3)} . \color{green}{(-q)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{1}{6}q+3q-3.\frac{1}{6}& \text{Uitwerken } \\ & =-q^2+(\frac{1}{6}+3)q-\frac{3}{6} & \text{Neem samen} \\ &=-q^2+\frac{19}{6}q-\frac{3}{6} & \text{Maak de som} \\ &=-q^2+\frac{19}{6}q-\frac{1}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-5}{19})(\frac{-2}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{-5}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{10}a-\frac{5}{19}a+\frac{5}{19}.\frac{1}{10}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{10})+(\frac{-5}{19}))a+\frac{5}{190} & \text{Neem samen} \\ &=a^2-\frac{69}{190}a+\frac{5}{190} & \text{Maak de som} \\ &=a^2-\frac{69}{190}a+\frac{1}{38} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(p-\frac{11}{6})(p-(-17))& =(\color{red}{p}+\color{orange}{\frac{-11}{6}}).(\color{green}{p}+\color{blue}{17})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(17)} + \color{orange}{(\frac{-11}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = pp+17p-\frac{11}{6}p-\frac{11}{6}.17& \text{Uitwerken } \\ & =p^2+(17+(\frac{-11}{6}))p-(\frac{-187}{6}) & \text{Neem samen} \\ &=p^2+\frac{91}{6}p-(\frac{-187}{6}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-11}{14})(\frac{-11}{8}+a)& =(\color{red}{a}+\color{orange}{\frac{-11}{14}}).(\color{green}{a}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{11}{8}a-\frac{11}{14}a+\frac{11}{14}.\frac{11}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-11}{8})+(\frac{-11}{14}))a+\frac{121}{112} & \text{Neem samen} \\ &=a^2-\frac{121}{56}a+\frac{121}{112} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-12}{8})(a-\frac{9}{3})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ab-3b+\frac{3}{2}a-\frac{3}{2}.3& \text{Uitwerken } \\ & =ab-3b+\frac{3}{2}a-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-11}{11})(\frac{2}{20}-b)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{10}x-1b+1.\frac{1}{10}& \text{Uitwerken } \\ & =-bx+\frac{1}{10}x-1b+\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{14}+b)(\frac{11}{13}+b)& =(\color{red}{b}+\color{orange}{\frac{-19}{14}}).(\color{green}{b}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{13}b-\frac{19}{14}b-\frac{19}{14}.\frac{11}{13}& \text{Uitwerken } \\ & =b^2+(\frac{11}{13}+(\frac{-19}{14}))b-(\frac{-209}{182}) & \text{Neem samen} \\ &=b^2-\frac{93}{182}b-(\frac{-209}{182}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-12}{17})(q+\frac{5}{18})& =(\color{red}{a}+\color{orange}{\frac{12}{17}}).(\color{green}{q}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{18}a+\frac{12}{17}q+\frac{12}{17}.\frac{5}{18}& \text{Uitwerken } \\ & =aq+\frac{5}{18}a+\frac{12}{17}q+\frac{60}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{18}a+\frac{12}{17}q+\frac{10}{51} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{17}+b)(q-\frac{18}{8})& =(\color{red}{b}+\color{orange}{\frac{-11}{17}}).(\color{green}{q}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{4}b-\frac{11}{17}q+\frac{11}{17}.\frac{9}{4}& \text{Uitwerken } \\ & =bq-\frac{9}{4}b-\frac{11}{17}q+\frac{99}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{1}{14})(\frac{-2}{19}+b)& =(\color{red}{a}+\color{orange}{\frac{1}{14}}).(\color{green}{b}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{1}{14})} . \color{green}{(b)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{19}a+\frac{1}{14}b-\frac{1}{14}.\frac{2}{19}& \text{Uitwerken } \\ & =ab-\frac{2}{19}a+\frac{1}{14}b-\frac{2}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{19}a+\frac{1}{14}b-\frac{1}{133} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-11-11 15:54:34
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