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

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  1. \((\frac{3}{3}+q)(x-\frac{-16}{6})\)
  2. \((\frac{-15}{7}-b)(b+\frac{13}{14})\)
  3. \((x+\frac{-16}{2})(a+\frac{-10}{9})\)
  4. \((a-(-11))(\frac{-3}{4}-q)\)
  5. \((\frac{-9}{17}-b)(x-\frac{-16}{3})\)
  6. \((\frac{20}{9}-x)(p-\frac{-13}{9})\)
  7. \((p-\frac{-2}{10})(x+\frac{3}{18})\)
  8. \((q+\frac{4}{10})(\frac{-3}{20}+a)\)
  9. \((x+\frac{-20}{20})(\frac{13}{18}-x)\)
  10. \((p+\frac{-14}{9})(b-\frac{11}{14})\)
  11. \((\frac{-14}{8}-x)(q+\frac{-11}{18})\)
  12. \((\frac{9}{16}+q)(\frac{18}{20}+q)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{3}+q)(x-\frac{-16}{6})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{3}q+1x+1.\frac{8}{3}& \text{Uitwerken } \\ & =qx+\frac{8}{3}q+1x+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-15}{7}-b)(b+\frac{13}{14})& =(\color{red}{-b}+\color{orange}{\frac{-15}{7}}).(\color{green}{b}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{13}{14}b-\frac{15}{7}b-\frac{15}{7}.\frac{13}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-13}{14})+(\frac{-15}{7}))b-\frac{195}{98} & \text{Neem samen} \\ &=-b^2-\frac{43}{14}b-\frac{195}{98} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-16}{2})(a+\frac{-10}{9})& =(\color{red}{x}+\color{orange}{(-8)}).(\color{green}{a}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(-8)} . \color{green}{(a)} + \color{orange}{(-8)} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{9}x-8a+8.\frac{10}{9}& \text{Uitwerken } \\ & =ax-\frac{10}{9}x-8a+\frac{80}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-(-11))(\frac{-3}{4}-q)& =(\color{red}{a}+\color{orange}{11}).(\color{green}{-q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(11)} . \color{green}{(-q)} + \color{orange}{(11)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{4}a-11q-11.\frac{3}{4}& \text{Uitwerken } \\ & =-aq-\frac{3}{4}a-11q-\frac{33}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{17}-b)(x-\frac{-16}{3})& =(\color{red}{-b}+\color{orange}{\frac{-9}{17}}).(\color{green}{x}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{3}b-\frac{9}{17}x-\frac{9}{17}.\frac{16}{3}& \text{Uitwerken } \\ & =-bx-\frac{16}{3}b-\frac{9}{17}x-\frac{144}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{16}{3}b-\frac{9}{17}x-\frac{48}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{9}-x)(p-\frac{-13}{9})& =(\color{red}{-x}+\color{orange}{\frac{20}{9}}).(\color{green}{p}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{20}{9})} . \color{green}{(p)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{9}x+\frac{20}{9}p+\frac{20}{9}.\frac{13}{9}& \text{Uitwerken } \\ & =-px-\frac{13}{9}x+\frac{20}{9}p+\frac{260}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-2}{10})(x+\frac{3}{18})& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{6}p+\frac{1}{5}x+\frac{1}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =px+\frac{1}{6}p+\frac{1}{5}x+\frac{1}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{4}{10})(\frac{-3}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{20}q+\frac{2}{5}a-\frac{2}{5}.\frac{3}{20}& \text{Uitwerken } \\ & =aq-\frac{3}{20}q+\frac{2}{5}a-\frac{6}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{3}{20}q+\frac{2}{5}a-\frac{3}{50} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-20}{20})(\frac{13}{18}-x)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{18}x+1x-1.\frac{13}{18}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{18}+1)x-\frac{13}{18} & \text{Neem samen} \\ &=-x^2+\frac{31}{18}x-\frac{13}{18} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-14}{9})(b-\frac{11}{14})& =(\color{red}{p}+\color{orange}{\frac{-14}{9}}).(\color{green}{b}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{14}p-\frac{14}{9}b+\frac{14}{9}.\frac{11}{14}& \text{Uitwerken } \\ & =bp-\frac{11}{14}p-\frac{14}{9}b+\frac{154}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{11}{14}p-\frac{14}{9}b+\frac{11}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{8}-x)(q+\frac{-11}{18})& =(\color{red}{-x}+\color{orange}{\frac{-7}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{18}x-\frac{7}{4}q+\frac{7}{4}.\frac{11}{18}& \text{Uitwerken } \\ & =-qx+\frac{11}{18}x-\frac{7}{4}q+\frac{77}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{16}+q)(\frac{18}{20}+q)& =(\color{red}{q}+\color{orange}{\frac{9}{16}}).(\color{green}{q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{9}{10}q+\frac{9}{16}q+\frac{9}{16}.\frac{9}{10}& \text{Uitwerken } \\ & =q^2+(\frac{9}{10}+\frac{9}{16})q+\frac{81}{160} & \text{Neem samen} \\ &=q^2+\frac{117}{80}q+\frac{81}{160} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-02 19:06:43
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