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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{8}-a)(\frac{-10}{20}+b)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{2}a-2b+2.\frac{1}{2}& \text{Uitwerken } \\ & =-ab+\frac{1}{2}a-2b+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{1}{2}a-2b+1 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{3}+b)(b+\frac{15}{13})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{15}{13}b-\frac{2}{3}b-\frac{2}{3}.\frac{15}{13}& \text{Uitwerken } \\ & =b^2+(\frac{15}{13}+(\frac{-2}{3}))b-(\frac{-30}{39}) & \text{Neem samen} \\ &=b^2+\frac{19}{39}b-(\frac{-30}{39}) & \text{Maak de som} \\ &=b^2+\frac{19}{39}b+\frac{10}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(a-\frac{6}{16})(\frac{12}{15}+a)& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{5}a-\frac{3}{8}a-\frac{3}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =a^2+(\frac{4}{5}+(\frac{-3}{8}))a-(\frac{-12}{40}) & \text{Neem samen} \\ &=a^2+\frac{17}{40}a-(\frac{-12}{40}) & \text{Maak de som} \\ &=a^2+\frac{17}{40}a+\frac{3}{10} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{12}-q)(a-\frac{15}{11})& =(\color{red}{-q}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{15}{11}q-\frac{5}{6}a+\frac{5}{6}.\frac{15}{11}& \text{Uitwerken } \\ & =-aq+\frac{15}{11}q-\frac{5}{6}a+\frac{75}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{15}{11}q-\frac{5}{6}a+\frac{25}{22} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{15}{12})(\frac{-20}{8}-q)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{-q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{2}p+\frac{5}{4}q+\frac{5}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =-pq-\frac{5}{2}p+\frac{5}{4}q+\frac{25}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-18}{6})(a-\frac{-12}{6})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2b-3a-3.2& \text{Uitwerken } \\ & =ab+2b-3a-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{14}+b)(x+\frac{3}{17})& =(\color{red}{b}+\color{orange}{\frac{-15}{14}}).(\color{green}{x}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{17}b-\frac{15}{14}x-\frac{15}{14}.\frac{3}{17}& \text{Uitwerken } \\ & =bx+\frac{3}{17}b-\frac{15}{14}x-\frac{45}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{17}{10})(\frac{19}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{-17}{10}}).(\color{green}{a}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{20}q-\frac{17}{10}a-\frac{17}{10}.\frac{19}{20}& \text{Uitwerken } \\ & =aq+\frac{19}{20}q-\frac{17}{10}a-\frac{323}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{19}{14})(\frac{-2}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{19}{14}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{19}{14})} . \color{green}{(b)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{5}q+\frac{19}{14}b-\frac{19}{14}.\frac{2}{5}& \text{Uitwerken } \\ & =bq-\frac{2}{5}q+\frac{19}{14}b-\frac{38}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{2}{5}q+\frac{19}{14}b-\frac{19}{35} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{11}+q)(\frac{-6}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{3}{11}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{3}{11})} . \color{green}{(a)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{3}q+\frac{3}{11}a-\frac{3}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =aq-\frac{2}{3}q+\frac{3}{11}a-\frac{6}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{2}{3}q+\frac{3}{11}a-\frac{2}{11} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q-\frac{15}{7})(\frac{-4}{15}-q)& =(\color{red}{q}+\color{orange}{\frac{-15}{7}}).(\color{green}{-q}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{4}{15}q+\frac{15}{7}q+\frac{15}{7}.\frac{4}{15}& \text{Uitwerken } \\ & =-q^2+((\frac{-4}{15})+\frac{15}{7})q+(\frac{-60}{105}) & \text{Neem samen} \\ &=-q^2+\frac{197}{105}q+(\frac{-60}{105}) & \text{Maak de som} \\ &=-q^2+\frac{197}{105}q+(\frac{-4}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(x-\frac{8}{7})(\frac{15}{9}+p)& =(\color{red}{x}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{3}x-\frac{8}{7}p-\frac{8}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =px+\frac{5}{3}x-\frac{8}{7}p-\frac{40}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-08 15:23:05
Een site van Busleyden Atheneum Mechelen