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

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  1. \((\frac{7}{11}+q)(q-\frac{11}{17})\)
  2. \((\frac{18}{2}+a)(a-\frac{-10}{14})\)
  3. \((\frac{11}{19}+b)(p-\frac{1}{18})\)
  4. \((\frac{-7}{2}-p)(\frac{-5}{15}+a)\)
  5. \((b-\frac{-2}{19})(\frac{-19}{18}-b)\)
  6. \((\frac{-10}{19}+q)(\frac{-19}{17}-a)\)
  7. \((\frac{13}{20}+a)(\frac{17}{5}+b)\)
  8. \((\frac{18}{15}+x)(\frac{-6}{17}+p)\)
  9. \((\frac{6}{19}-x)(\frac{7}{20}+b)\)
  10. \((p-\frac{-16}{20})(x+\frac{-20}{8})\)
  11. \((\frac{-9}{3}+p)(\frac{2}{4}+q)\)
  12. \((\frac{5}{4}+a)(x+\frac{-13}{8})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{11}+q)(q-\frac{11}{17})& =(\color{red}{q}+\color{orange}{\frac{7}{11}}).(\color{green}{q}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{7}{11})} . \color{green}{(q)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{17}q+\frac{7}{11}q-\frac{7}{11}.\frac{11}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{17})+\frac{7}{11})q-(\frac{-77}{187}) & \text{Neem samen} \\ &=q^2-\frac{2}{187}q-(\frac{-77}{187}) & \text{Maak de som} \\ &=q^2-\frac{2}{187}q+\frac{7}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{2}+a)(a-\frac{-10}{14})& =(\color{red}{a}+\color{orange}{9}).(\color{green}{a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(9)} . \color{green}{(a)} + \color{orange}{(9)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{7}a+9a+9.\frac{5}{7}& \text{Uitwerken } \\ & =a^2+(\frac{5}{7}+9)a+\frac{45}{7} & \text{Neem samen} \\ &=a^2+\frac{68}{7}a+\frac{45}{7} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{19}+b)(p-\frac{1}{18})& =(\color{red}{b}+\color{orange}{\frac{11}{19}}).(\color{green}{p}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{11}{19})} . \color{green}{(p)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{18}b+\frac{11}{19}p-\frac{11}{19}.\frac{1}{18}& \text{Uitwerken } \\ & =bp-\frac{1}{18}b+\frac{11}{19}p-\frac{11}{342} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{2}-p)(\frac{-5}{15}+a)& =(\color{red}{-p}+\color{orange}{\frac{-7}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{3}p-\frac{7}{2}a+\frac{7}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =-ap+\frac{1}{3}p-\frac{7}{2}a+\frac{7}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-2}{19})(\frac{-19}{18}-b)& =(\color{red}{b}+\color{orange}{\frac{2}{19}}).(\color{green}{-b}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{2}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{18}b-\frac{2}{19}b-\frac{2}{19}.\frac{19}{18}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{18})+(\frac{-2}{19}))b-\frac{38}{342} & \text{Neem samen} \\ &=-b^2-\frac{397}{342}b-\frac{38}{342} & \text{Maak de som} \\ &=-b^2-\frac{397}{342}b-\frac{1}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-10}{19}+q)(\frac{-19}{17}-a)& =(\color{red}{q}+\color{orange}{\frac{-10}{19}}).(\color{green}{-a}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{17}q+\frac{10}{19}a+\frac{10}{19}.\frac{19}{17}& \text{Uitwerken } \\ & =-aq-\frac{19}{17}q+\frac{10}{19}a+\frac{190}{323} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{19}{17}q+\frac{10}{19}a+\frac{10}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{20}+a)(\frac{17}{5}+b)& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{5}a+\frac{13}{20}b+\frac{13}{20}.\frac{17}{5}& \text{Uitwerken } \\ & =ab+\frac{17}{5}a+\frac{13}{20}b+\frac{221}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{15}+x)(\frac{-6}{17}+p)& =(\color{red}{x}+\color{orange}{\frac{6}{5}}).(\color{green}{p}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{17}x+\frac{6}{5}p-\frac{6}{5}.\frac{6}{17}& \text{Uitwerken } \\ & =px-\frac{6}{17}x+\frac{6}{5}p-\frac{36}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{19}-x)(\frac{7}{20}+b)& =(\color{red}{-x}+\color{orange}{\frac{6}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{20}x+\frac{6}{19}b+\frac{6}{19}.\frac{7}{20}& \text{Uitwerken } \\ & =-bx-\frac{7}{20}x+\frac{6}{19}b+\frac{42}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{7}{20}x+\frac{6}{19}b+\frac{21}{190} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-16}{20})(x+\frac{-20}{8})& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{2}p+\frac{4}{5}x-\frac{4}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =px-\frac{5}{2}p+\frac{4}{5}x-\frac{20}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{2}p+\frac{4}{5}x-2 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{3}+p)(\frac{2}{4}+q)& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}p-3q-3.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}p-3q-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{4}+a)(x+\frac{-13}{8})& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{8}a+\frac{5}{4}x-\frac{5}{4}.\frac{13}{8}& \text{Uitwerken } \\ & =ax-\frac{13}{8}a+\frac{5}{4}x-\frac{65}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-19 11:39:06
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