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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{7}+p)(\frac{-5}{20}+p)& =(\color{red}{p}+\color{orange}{\frac{-18}{7}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{4}p-\frac{18}{7}p+\frac{18}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{4})+(\frac{-18}{7}))p+\frac{18}{28} & \text{Neem samen} \\ &=p^2-\frac{79}{28}p+\frac{18}{28} & \text{Maak de som} \\ &=p^2-\frac{79}{28}p+\frac{9}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-5}{5})(p+\frac{-15}{12})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{4}p+1p-1.\frac{5}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{4})+1)p-(\frac{-5}{4}) & \text{Neem samen} \\ &=p^2-\frac{1}{4}p-(\frac{-5}{4}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(p-\frac{18}{5})(\frac{3}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{-18}{5}}).(\color{green}{q}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{17}p-\frac{18}{5}q-\frac{18}{5}.\frac{3}{17}& \text{Uitwerken } \\ & =pq+\frac{3}{17}p-\frac{18}{5}q-\frac{54}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{3}+b)(q-(-1))& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-\frac{5}{3}q-\frac{5}{3}.1& \text{Uitwerken } \\ & =bq+1b-\frac{5}{3}q-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{14}{14})(\frac{17}{14}+b)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{14}x+1b+1.\frac{17}{14}& \text{Uitwerken } \\ & =bx+\frac{17}{14}x+1b+\frac{17}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-12}{19})(\frac{12}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{12}{19}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{12}{19})} . \color{green}{(q)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = aq+6a+\frac{12}{19}q+\frac{12}{19}.6& \text{Uitwerken } \\ & =aq+6a+\frac{12}{19}q+\frac{72}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-13}{17}-p)(\frac{-6}{11}-a)& =(\color{red}{-p}+\color{orange}{\frac{-13}{17}}).(\color{green}{-a}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{11}p+\frac{13}{17}a+\frac{13}{17}.\frac{6}{11}& \text{Uitwerken } \\ & =ap+\frac{6}{11}p+\frac{13}{17}a+\frac{78}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}((-11)-x)(p-17)& =(\color{red}{-x}+\color{orange}{(-11)}).(\color{green}{p}+\color{blue}{(-17)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(-17)} + \color{orange}{(-11)} . \color{green}{(p)} + \color{orange}{(-11)} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = -px+17x-11p+11.17& \text{Uitwerken } \\ & =-px+17x-11p+187 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{7}+x)(a+\frac{-19}{4})& =(\color{red}{x}+\color{orange}{\frac{-10}{7}}).(\color{green}{a}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{4}x-\frac{10}{7}a+\frac{10}{7}.\frac{19}{4}& \text{Uitwerken } \\ & =ax-\frac{19}{4}x-\frac{10}{7}a+\frac{190}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{19}{4}x-\frac{10}{7}a+\frac{95}{14} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{12}-q)(\frac{16}{17}+b)& =(\color{red}{-q}+\color{orange}{\frac{5}{6}}).(\color{green}{b}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{17}q+\frac{5}{6}b+\frac{5}{6}.\frac{16}{17}& \text{Uitwerken } \\ & =-bq-\frac{16}{17}q+\frac{5}{6}b+\frac{80}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{16}{17}q+\frac{5}{6}b+\frac{40}{51} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{12}+x)(\frac{-18}{13}-b)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{-b}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{18}{13}x+\frac{5}{3}b+\frac{5}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =-bx-\frac{18}{13}x+\frac{5}{3}b+\frac{90}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{18}{13}x+\frac{5}{3}b+\frac{30}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-18}{4})(b+\frac{-4}{18})& =(\color{red}{a}+\color{orange}{\frac{9}{2}}).(\color{green}{b}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{9}a+\frac{9}{2}b-\frac{9}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =ab-\frac{2}{9}a+\frac{9}{2}b-\frac{18}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{9}a+\frac{9}{2}b-1 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-26 05:09:42
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