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

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

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Verbetersleutel

  1. \(\begin{align}(b+\frac{-13}{11})(\frac{14}{18}-x)& =(\color{red}{b}+\color{orange}{\frac{-13}{11}}).(\color{green}{-x}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{9}b+\frac{13}{11}x-\frac{13}{11}.\frac{7}{9}& \text{Uitwerken } \\ & =-bx+\frac{7}{9}b+\frac{13}{11}x-\frac{91}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-6}{2})(\frac{8}{8}+b)& =(\color{red}{a}+\color{orange}{3}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1a+3b+3.1& \text{Uitwerken } \\ & =ab+1a+3b+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{4}-b)(p+\frac{1}{9})& =(\color{red}{-b}+\color{orange}{\frac{-15}{4}}).(\color{green}{p}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{9}b-\frac{15}{4}p-\frac{15}{4}.\frac{1}{9}& \text{Uitwerken } \\ & =-bp-\frac{1}{9}b-\frac{15}{4}p-\frac{15}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{1}{9}b-\frac{15}{4}p-\frac{5}{12} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-12}{5})(\frac{18}{6}+q)& =(\color{red}{q}+\color{orange}{\frac{12}{5}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{12}{5})} . \color{green}{(q)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qq+3q+\frac{12}{5}q+\frac{12}{5}.3& \text{Uitwerken } \\ & =q^2+(3+\frac{12}{5})q+\frac{36}{5} & \text{Neem samen} \\ &=q^2+\frac{27}{5}q+\frac{36}{5} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{13}-b)(q+\frac{3}{18})& =(\color{red}{-b}+\color{orange}{\frac{-6}{13}}).(\color{green}{q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{6}b-\frac{6}{13}q-\frac{6}{13}.\frac{1}{6}& \text{Uitwerken } \\ & =-bq-\frac{1}{6}b-\frac{6}{13}q-\frac{6}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{6}b-\frac{6}{13}q-\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{14}{4}-x)(\frac{5}{5}+p)& =(\color{red}{-x}+\color{orange}{\frac{7}{2}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px-1x+\frac{7}{2}p+\frac{7}{2}.1& \text{Uitwerken } \\ & =-px-1x+\frac{7}{2}p+\frac{7}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-18}{12})(q+\frac{17}{13})& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{13}x+\frac{3}{2}q+\frac{3}{2}.\frac{17}{13}& \text{Uitwerken } \\ & =qx+\frac{17}{13}x+\frac{3}{2}q+\frac{51}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-13}{17})(q-\frac{-14}{17})& =(\color{red}{x}+\color{orange}{\frac{13}{17}}).(\color{green}{q}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{14}{17}x+\frac{13}{17}q+\frac{13}{17}.\frac{14}{17}& \text{Uitwerken } \\ & =qx+\frac{14}{17}x+\frac{13}{17}q+\frac{182}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{2}+a)(\frac{18}{18}+b)& =(\color{red}{a}+\color{orange}{\frac{-19}{2}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1a-\frac{19}{2}b-\frac{19}{2}.1& \text{Uitwerken } \\ & =ab+1a-\frac{19}{2}b-\frac{19}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-7}{18})(\frac{20}{11}+b)& =(\color{red}{b}+\color{orange}{\frac{7}{18}}).(\color{green}{b}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{20}{11}b+\frac{7}{18}b+\frac{7}{18}.\frac{20}{11}& \text{Uitwerken } \\ & =b^2+(\frac{20}{11}+\frac{7}{18})b+\frac{140}{198} & \text{Neem samen} \\ &=b^2+\frac{437}{198}b+\frac{140}{198} & \text{Maak de som} \\ &=b^2+\frac{437}{198}b+\frac{70}{99} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{11}-q)(x+\frac{10}{15})& =(\color{red}{-q}+\color{orange}{\frac{18}{11}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{18}{11})} . \color{green}{(x)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{3}q+\frac{18}{11}x+\frac{18}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =-qx-\frac{2}{3}q+\frac{18}{11}x+\frac{36}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{2}{3}q+\frac{18}{11}x+\frac{12}{11} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{5}+a)(6-p)& =(\color{red}{a}+\color{orange}{\frac{12}{5}}).(\color{green}{-p}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{12}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -ap+6a-\frac{12}{5}p+\frac{12}{5}.6& \text{Uitwerken } \\ & =-ap+6a-\frac{12}{5}p+\frac{72}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-01 13:29:41
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