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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{10}+x)(a+4)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ax+4x+2a+2.4& \text{Uitwerken } \\ & =ax+4x+2a+8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{18}{12})(\frac{-6}{3}+a)& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b+\frac{3}{2}a-\frac{3}{2}.2& \text{Uitwerken } \\ & =ab-2b+\frac{3}{2}a-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-2b+\frac{3}{2}a-3 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{12}{14})(a+\frac{2}{17})& =(\color{red}{x}+\color{orange}{\frac{-6}{7}}).(\color{green}{a}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{17}x-\frac{6}{7}a-\frac{6}{7}.\frac{2}{17}& \text{Uitwerken } \\ & =ax+\frac{2}{17}x-\frac{6}{7}a-\frac{12}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-14}{17}+q)((-17)-a)& =(\color{red}{q}+\color{orange}{\frac{-14}{17}}).(\color{green}{-a}+\color{blue}{(-17)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-17)} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = -aq-17q+\frac{14}{17}a+\frac{14}{17}.17& \text{Uitwerken } \\ & =-aq-17q+\frac{14}{17}a+\frac{238}{17} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-17q+\frac{14}{17}a+14 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-20}{14})(a+\frac{-19}{19})& =(\color{red}{q}+\color{orange}{\frac{-10}{7}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1q-\frac{10}{7}a+\frac{10}{7}.1& \text{Uitwerken } \\ & =aq-1q-\frac{10}{7}a+\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{9}-a)(q-\frac{2}{6})& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{3}a+\frac{1}{3}q-\frac{1}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =-aq+\frac{1}{3}a+\frac{1}{3}q-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-15}{3})(\frac{5}{7}+b)& =(\color{red}{p}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{7}p+5b+5.\frac{5}{7}& \text{Uitwerken } \\ & =bp+\frac{5}{7}p+5b+\frac{25}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{7}+b)(b+\frac{18}{20})& =(\color{red}{b}+\color{orange}{\frac{13}{7}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{13}{7})} . \color{green}{(b)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{10}b+\frac{13}{7}b+\frac{13}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =b^2+(\frac{9}{10}+\frac{13}{7})b+\frac{117}{70} & \text{Neem samen} \\ &=b^2+\frac{193}{70}b+\frac{117}{70} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{1}{8}-p)(\frac{-13}{12}+a)& =(\color{red}{-p}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{12}p+\frac{1}{8}a-\frac{1}{8}.\frac{13}{12}& \text{Uitwerken } \\ & =-ap+\frac{13}{12}p+\frac{1}{8}a-\frac{13}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{11}{11})(\frac{-3}{14}-a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{14}b-1a-1.\frac{3}{14}& \text{Uitwerken } \\ & =-ab-\frac{3}{14}b-1a-\frac{3}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{18}{5})(\frac{-11}{9}-b)& =(\color{red}{p}+\color{orange}{\frac{-18}{5}}).(\color{green}{-b}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{9}p+\frac{18}{5}b+\frac{18}{5}.\frac{11}{9}& \text{Uitwerken } \\ & =-bp-\frac{11}{9}p+\frac{18}{5}b+\frac{198}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{11}{9}p+\frac{18}{5}b+\frac{22}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{7}-q)(\frac{12}{6}+q)& =(\color{red}{-q}+\color{orange}{\frac{-3}{7}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qq-2q-\frac{3}{7}q-\frac{3}{7}.2& \text{Uitwerken } \\ & =-q^2+((-2)+(\frac{-3}{7}))q-\frac{6}{7} & \text{Neem samen} \\ &=-q^2-\frac{17}{7}q-\frac{6}{7} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-14 11:37:59
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