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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-4}{12})(\frac{-7}{17}-a)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{-a}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{17}x-\frac{1}{3}a-\frac{1}{3}.\frac{7}{17}& \text{Uitwerken } \\ & =-ax-\frac{7}{17}x-\frac{1}{3}a-\frac{7}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{15}{2})(x+\frac{18}{4})& =(\color{red}{x}+\color{orange}{\frac{-15}{2}}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{2}x-\frac{15}{2}x-\frac{15}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =x^2+(\frac{9}{2}+(\frac{-15}{2}))x-(\frac{-135}{4}) & \text{Neem samen} \\ &=x^2-\frac{6}{2}x-(\frac{-135}{4}) & \text{Maak de som} \\ &=x^2-3x+\frac{135}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(a+\frac{12}{17})(\frac{-9}{3}-b)& =(\color{red}{a}+\color{orange}{\frac{12}{17}}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{12}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -ab-3a-\frac{12}{17}b-\frac{12}{17}.3& \text{Uitwerken } \\ & =-ab-3a-\frac{12}{17}b-\frac{36}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{14}+q)(\frac{-3}{19}-x)& =(\color{red}{q}+\color{orange}{\frac{-13}{14}}).(\color{green}{-x}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{19}q+\frac{13}{14}x+\frac{13}{14}.\frac{3}{19}& \text{Uitwerken } \\ & =-qx-\frac{3}{19}q+\frac{13}{14}x+\frac{39}{266} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{13}{6})(a-\frac{-9}{12})& =(\color{red}{p}+\color{orange}{\frac{-13}{6}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}p-\frac{13}{6}a-\frac{13}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}p-\frac{13}{6}a-\frac{39}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{4}p-\frac{13}{6}a-\frac{13}{8} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-15}{15})(\frac{-18}{19}-q)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{18}{19}b+1q+1.\frac{18}{19}& \text{Uitwerken } \\ & =-bq-\frac{18}{19}b+1q+\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{3}{9})(q-7)& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-7)} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = pq-7p+\frac{1}{3}q-\frac{1}{3}.7& \text{Uitwerken } \\ & =pq-7p+\frac{1}{3}q-\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-2}{3})(p-\frac{15}{12})& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{4}x-\frac{2}{3}p+\frac{2}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =px-\frac{5}{4}x-\frac{2}{3}p+\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{4}x-\frac{2}{3}p+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-12}{18})(a+\frac{-1}{19})& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{19}a-\frac{2}{3}a+\frac{2}{3}.\frac{1}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{19})+(\frac{-2}{3}))a+\frac{2}{57} & \text{Neem samen} \\ &=a^2-\frac{41}{57}a+\frac{2}{57} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-2}{15})(\frac{-19}{20}-b)& =(\color{red}{q}+\color{orange}{\frac{2}{15}}).(\color{green}{-b}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{2}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{19}{20}q-\frac{2}{15}b-\frac{2}{15}.\frac{19}{20}& \text{Uitwerken } \\ & =-bq-\frac{19}{20}q-\frac{2}{15}b-\frac{38}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{19}{20}q-\frac{2}{15}b-\frac{19}{150} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{2}{13})(\frac{4}{5}-b)& =(\color{red}{b}+\color{orange}{\frac{2}{13}}).(\color{green}{-b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{2}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{4}{5}b-\frac{2}{13}b+\frac{2}{13}.\frac{4}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{4}{5}+(\frac{-2}{13}))b+(\frac{-8}{65}) & \text{Neem samen} \\ &=-b^2+\frac{42}{65}b+(\frac{-8}{65}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-13}{17}-q)(p-\frac{19}{3})& =(\color{red}{-q}+\color{orange}{\frac{-13}{17}}).(\color{green}{p}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{19}{3}q-\frac{13}{17}p+\frac{13}{17}.\frac{19}{3}& \text{Uitwerken } \\ & =-pq+\frac{19}{3}q-\frac{13}{17}p+\frac{247}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-23 02:04:32
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