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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-6}{18})(\frac{-5}{7}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{7}x+\frac{1}{3}b-\frac{1}{3}.\frac{5}{7}& \text{Uitwerken } \\ & =bx-\frac{5}{7}x+\frac{1}{3}b-\frac{5}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-6}{16}+q)(\frac{-4}{4}+b)& =(\color{red}{q}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1q-\frac{3}{8}b+\frac{3}{8}.1& \text{Uitwerken } \\ & =bq-1q-\frac{3}{8}b+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{8}+a)(a-\frac{18}{5})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{18}{5}a-2a+2.\frac{18}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-18}{5})+(-2))a+\frac{36}{5} & \text{Neem samen} \\ &=a^2-\frac{28}{5}a+\frac{36}{5} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-13}{13})(\frac{15}{19}+a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{19}b+1a+1.\frac{15}{19}& \text{Uitwerken } \\ & =ab+\frac{15}{19}b+1a+\frac{15}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{1}{10}-a)(x-\frac{-14}{11})& =(\color{red}{-a}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{14}{11}a+\frac{1}{10}x+\frac{1}{10}.\frac{14}{11}& \text{Uitwerken } \\ & =-ax-\frac{14}{11}a+\frac{1}{10}x+\frac{14}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{14}{11}a+\frac{1}{10}x+\frac{7}{55} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{19}{11}-q)(\frac{3}{4}-p)& =(\color{red}{-q}+\color{orange}{\frac{19}{11}}).(\color{green}{-p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{19}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{4}q-\frac{19}{11}p+\frac{19}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =pq-\frac{3}{4}q-\frac{19}{11}p+\frac{57}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{17}{10})(\frac{-17}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{17}{10}}).(\color{green}{p}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{4}a+\frac{17}{10}p-\frac{17}{10}.\frac{17}{4}& \text{Uitwerken } \\ & =ap-\frac{17}{4}a+\frac{17}{10}p-\frac{289}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-12}{17})(a+\frac{-7}{12})& =(\color{red}{p}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{12}p+\frac{12}{17}a-\frac{12}{17}.\frac{7}{12}& \text{Uitwerken } \\ & =ap-\frac{7}{12}p+\frac{12}{17}a-\frac{84}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{7}{12}p+\frac{12}{17}a-\frac{7}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-13}{15})(\frac{14}{4}-p)& =(\color{red}{b}+\color{orange}{\frac{13}{15}}).(\color{green}{-p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{13}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{2}b-\frac{13}{15}p+\frac{13}{15}.\frac{7}{2}& \text{Uitwerken } \\ & =-bp+\frac{7}{2}b-\frac{13}{15}p+\frac{91}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{18}+b)(x+\frac{3}{6})& =(\color{red}{b}+\color{orange}{\frac{-4}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}b-\frac{4}{9}x-\frac{4}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}b-\frac{4}{9}x-\frac{4}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{1}{2}b-\frac{4}{9}x-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{19}+x)(\frac{-9}{4}+a)& =(\color{red}{x}+\color{orange}{\frac{-14}{19}}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{4}x-\frac{14}{19}a+\frac{14}{19}.\frac{9}{4}& \text{Uitwerken } \\ & =ax-\frac{9}{4}x-\frac{14}{19}a+\frac{126}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{4}x-\frac{14}{19}a+\frac{63}{38} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{6}+q)(\frac{-6}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{7}{6}}).(\color{green}{-q}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{6}{19}q-\frac{7}{6}q-\frac{7}{6}.\frac{6}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-6}{19})+(\frac{-7}{6}))q-\frac{42}{114} & \text{Neem samen} \\ &=-q^2-\frac{169}{114}q-\frac{42}{114} & \text{Maak de som} \\ &=-q^2-\frac{169}{114}q-\frac{7}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-31 20:01:57
Een site van Busleyden Atheneum Mechelen