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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{18}-a)(\frac{-3}{4}-p)& =(\color{red}{-a}+\color{orange}{\frac{-2}{9}}).(\color{green}{-p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}a+\frac{2}{9}p+\frac{2}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}a+\frac{2}{9}p+\frac{6}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{4}a+\frac{2}{9}p+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{1}{15})(\frac{-12}{2}-q)& =(\color{red}{p}+\color{orange}{\frac{1}{15}}).(\color{green}{-q}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-6)} + \color{orange}{(\frac{1}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -pq-6p-\frac{1}{15}q-\frac{1}{15}.6& \text{Uitwerken } \\ & =-pq-6p-\frac{1}{15}q-\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-6p-\frac{1}{15}q-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{18}-b)(x-\frac{18}{2})& =(\color{red}{-b}+\color{orange}{\frac{19}{18}}).(\color{green}{x}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-9)} + \color{orange}{(\frac{19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -bx+9b+\frac{19}{18}x-\frac{19}{18}.9& \text{Uitwerken } \\ & =-bx+9b+\frac{19}{18}x-\frac{171}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+9b+\frac{19}{18}x-\frac{19}{2} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-19}{10}+q)(\frac{20}{18}+q)& =(\color{red}{q}+\color{orange}{\frac{-19}{10}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{10}{9}q-\frac{19}{10}q-\frac{19}{10}.\frac{10}{9}& \text{Uitwerken } \\ & =q^2+(\frac{10}{9}+(\frac{-19}{10}))q-(\frac{-190}{90}) & \text{Neem samen} \\ &=q^2-\frac{71}{90}q-(\frac{-190}{90}) & \text{Maak de som} \\ &=q^2-\frac{71}{90}q+\frac{19}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-13}{14})(\frac{15}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-13}{14}}).(\color{green}{a}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{15}{2}x-\frac{13}{14}a-\frac{13}{14}.\frac{15}{2}& \text{Uitwerken } \\ & =ax+\frac{15}{2}x-\frac{13}{14}a-\frac{195}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{12}{17})(\frac{-1}{2}-b)& =(\color{red}{b}+\color{orange}{\frac{12}{17}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{12}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{2}b-\frac{12}{17}b-\frac{12}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{2})+(\frac{-12}{17}))b-\frac{12}{34} & \text{Neem samen} \\ &=-b^2-\frac{41}{34}b-\frac{12}{34} & \text{Maak de som} \\ &=-b^2-\frac{41}{34}b-\frac{6}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{12}-b)(p-\frac{-19}{4})& =(\color{red}{-b}+\color{orange}{\frac{5}{12}}).(\color{green}{p}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{5}{12})} . \color{green}{(p)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{4}b+\frac{5}{12}p+\frac{5}{12}.\frac{19}{4}& \text{Uitwerken } \\ & =-bp-\frac{19}{4}b+\frac{5}{12}p+\frac{95}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-3}{3})(\frac{10}{11}+q)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{11}a+1q+1.\frac{10}{11}& \text{Uitwerken } \\ & =aq+\frac{10}{11}a+1q+\frac{10}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{19}-b)(\frac{1}{16}+q)& =(\color{red}{-b}+\color{orange}{\frac{9}{19}}).(\color{green}{q}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{9}{19})} . \color{green}{(q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{16}b+\frac{9}{19}q+\frac{9}{19}.\frac{1}{16}& \text{Uitwerken } \\ & =-bq-\frac{1}{16}b+\frac{9}{19}q+\frac{9}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{19}+a)(8-x)& =(\color{red}{a}+\color{orange}{\frac{16}{19}}).(\color{green}{-x}+\color{blue}{8})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{16}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -ax+8a-\frac{16}{19}x+\frac{16}{19}.8& \text{Uitwerken } \\ & =-ax+8a-\frac{16}{19}x+\frac{128}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-3}{14})(\frac{-19}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-3}{14}}).(\color{green}{b}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{-3}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{12}p-\frac{3}{14}b+\frac{3}{14}.\frac{19}{12}& \text{Uitwerken } \\ & =bp-\frac{19}{12}p-\frac{3}{14}b+\frac{57}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{19}{12}p-\frac{3}{14}b+\frac{19}{56} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{19}+p)(\frac{-11}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{13}{19}}).(\color{green}{-q}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{20}p-\frac{13}{19}q-\frac{13}{19}.\frac{11}{20}& \text{Uitwerken } \\ & =-pq-\frac{11}{20}p-\frac{13}{19}q-\frac{143}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-31 13:18:35
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