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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{13}+b)(x-\frac{-10}{19})& =(\color{red}{b}+\color{orange}{\frac{12}{13}}).(\color{green}{x}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{12}{13})} . \color{green}{(x)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{19}b+\frac{12}{13}x+\frac{12}{13}.\frac{10}{19}& \text{Uitwerken } \\ & =bx+\frac{10}{19}b+\frac{12}{13}x+\frac{120}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{3}{2})(x+\frac{1}{10})& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{10}p+\frac{3}{2}x+\frac{3}{2}.\frac{1}{10}& \text{Uitwerken } \\ & =px+\frac{1}{10}p+\frac{3}{2}x+\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-18}{18})(\frac{8}{19}-b)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{19}q-1b+1.\frac{8}{19}& \text{Uitwerken } \\ & =-bq+\frac{8}{19}q-1b+\frac{8}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-17}{14})(a+\frac{-18}{2})& =(\color{red}{b}+\color{orange}{\frac{-17}{14}}).(\color{green}{a}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(\frac{-17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = ab-9b-\frac{17}{14}a+\frac{17}{14}.9& \text{Uitwerken } \\ & =ab-9b-\frac{17}{14}a+\frac{153}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{10}-a)(\frac{-16}{6}-a)& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{8}{3}a-2a-2.\frac{8}{3}& \text{Uitwerken } \\ & =a^2+(\frac{8}{3}+(-2))a-(\frac{-16}{3}) & \text{Neem samen} \\ &=a^2+\frac{2}{3}a-(\frac{-16}{3}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{8}+b)(\frac{20}{14}-q)& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{-q}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{10}{7}b-\frac{5}{2}q+\frac{5}{2}.\frac{10}{7}& \text{Uitwerken } \\ & =-bq+\frac{10}{7}b-\frac{5}{2}q+\frac{50}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{10}{7}b-\frac{5}{2}q+\frac{25}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-20}{6})(\frac{13}{14}-p)& =(\color{red}{p}+\color{orange}{\frac{-10}{3}}).(\color{green}{-p}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{13}{14}p+\frac{10}{3}p-\frac{10}{3}.\frac{13}{14}& \text{Uitwerken } \\ & =-p^2+(\frac{13}{14}+\frac{10}{3})p-\frac{130}{42} & \text{Neem samen} \\ &=-p^2+\frac{179}{42}p-\frac{130}{42} & \text{Maak de som} \\ &=-p^2+\frac{179}{42}p-\frac{65}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{5}{10}+b)(b-\frac{3}{14})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{14}b+\frac{1}{2}b-\frac{1}{2}.\frac{3}{14}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{14})+\frac{1}{2})b-(\frac{-3}{28}) & \text{Neem samen} \\ &=b^2+\frac{4}{14}b-(\frac{-3}{28}) & \text{Maak de som} \\ &=b^2+\frac{2}{7}b+\frac{3}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(b-\frac{3}{16})(p-\frac{5}{14})& =(\color{red}{b}+\color{orange}{\frac{-3}{16}}).(\color{green}{p}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{14}b-\frac{3}{16}p+\frac{3}{16}.\frac{5}{14}& \text{Uitwerken } \\ & =bp-\frac{5}{14}b-\frac{3}{16}p+\frac{15}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{7}{5})(\frac{-1}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{19}x-\frac{7}{5}a+\frac{7}{5}.\frac{1}{19}& \text{Uitwerken } \\ & =ax-\frac{1}{19}x-\frac{7}{5}a+\frac{7}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{9}-a)(\frac{13}{5}+b)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{13}{5}a-1b-1.\frac{13}{5}& \text{Uitwerken } \\ & =-ab-\frac{13}{5}a-1b-\frac{13}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{7}-q)(\frac{2}{17}+p)& =(\color{red}{-q}+\color{orange}{\frac{-15}{7}}).(\color{green}{p}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{17}q-\frac{15}{7}p-\frac{15}{7}.\frac{2}{17}& \text{Uitwerken } \\ & =-pq-\frac{2}{17}q-\frac{15}{7}p-\frac{30}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-09 08:01:13
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