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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-2}{9})(b+\frac{-15}{16})& =(\color{red}{p}+\color{orange}{\frac{2}{9}}).(\color{green}{b}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{15}{16}p+\frac{2}{9}b-\frac{2}{9}.\frac{15}{16}& \text{Uitwerken } \\ & =bp-\frac{15}{16}p+\frac{2}{9}b-\frac{30}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{15}{16}p+\frac{2}{9}b-\frac{5}{24} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-2}{11})(\frac{-1}{16}-x)& =(\color{red}{x}+\color{orange}{\frac{2}{11}}).(\color{green}{-x}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{2}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{1}{16}x-\frac{2}{11}x-\frac{2}{11}.\frac{1}{16}& \text{Uitwerken } \\ & =-x^2+((\frac{-1}{16})+(\frac{-2}{11}))x-\frac{2}{176} & \text{Neem samen} \\ &=-x^2-\frac{43}{176}x-\frac{2}{176} & \text{Maak de som} \\ &=-x^2-\frac{43}{176}x-\frac{1}{88} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{13}+a)(b+\frac{-18}{8})& =(\color{red}{a}+\color{orange}{\frac{11}{13}}).(\color{green}{b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{11}{13})} . \color{green}{(b)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{4}a+\frac{11}{13}b-\frac{11}{13}.\frac{9}{4}& \text{Uitwerken } \\ & =ab-\frac{9}{4}a+\frac{11}{13}b-\frac{99}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-7}{15})(\frac{-2}{14}+p)& =(\color{red}{q}+\color{orange}{\frac{-7}{15}}).(\color{green}{p}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{7}q-\frac{7}{15}p+\frac{7}{15}.\frac{1}{7}& \text{Uitwerken } \\ & =pq-\frac{1}{7}q-\frac{7}{15}p+\frac{7}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{7}q-\frac{7}{15}p+\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-11}{11}+b)(a-\frac{-7}{2})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{2}b-1a-1.\frac{7}{2}& \text{Uitwerken } \\ & =ab+\frac{7}{2}b-1a-\frac{7}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{14}+x)(p+\frac{-17}{12})& =(\color{red}{x}+\color{orange}{\frac{5}{14}}).(\color{green}{p}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{12}x+\frac{5}{14}p-\frac{5}{14}.\frac{17}{12}& \text{Uitwerken } \\ & =px-\frac{17}{12}x+\frac{5}{14}p-\frac{85}{168} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{19}-q)(13-q)& =(\color{red}{-q}+\color{orange}{\frac{12}{19}}).(\color{green}{-q}+\color{blue}{13})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(13)} + \color{orange}{(\frac{12}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = qq-13q-\frac{12}{19}q+\frac{12}{19}.13& \text{Uitwerken } \\ & =q^2+((-13)+(\frac{-12}{19}))q+\frac{156}{19} & \text{Neem samen} \\ &=q^2-\frac{259}{19}q+\frac{156}{19} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a+\frac{14}{20})(\frac{-16}{15}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{10}}).(\color{green}{p}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{15}a+\frac{7}{10}p-\frac{7}{10}.\frac{16}{15}& \text{Uitwerken } \\ & =ap-\frac{16}{15}a+\frac{7}{10}p-\frac{112}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{16}{15}a+\frac{7}{10}p-\frac{56}{75} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{3}-p)(\frac{4}{8}+p)& =(\color{red}{-p}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{2}p-5p-5.\frac{1}{2}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{2})+(-5))p-\frac{5}{2} & \text{Neem samen} \\ &=-p^2-\frac{11}{2}p-\frac{5}{2} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{7}+q)(\frac{-19}{16}+q)& =(\color{red}{q}+\color{orange}{\frac{16}{7}}).(\color{green}{q}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{16}{7})} . \color{green}{(q)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{16}q+\frac{16}{7}q-\frac{16}{7}.\frac{19}{16}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{16})+\frac{16}{7})q-(\frac{-304}{112}) & \text{Neem samen} \\ &=q^2+\frac{123}{112}q-(\frac{-304}{112}) & \text{Maak de som} \\ &=q^2+\frac{123}{112}q+\frac{19}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-19}{17})(\frac{-10}{9}-x)& =(\color{red}{b}+\color{orange}{\frac{-19}{17}}).(\color{green}{-x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{10}{9}b+\frac{19}{17}x+\frac{19}{17}.\frac{10}{9}& \text{Uitwerken } \\ & =-bx-\frac{10}{9}b+\frac{19}{17}x+\frac{190}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{7}+b)(\frac{-14}{3}-x)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{14}{3}b-2x-2.\frac{14}{3}& \text{Uitwerken } \\ & =-bx-\frac{14}{3}b-2x-\frac{28}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-18 21:59:35
Een site van Busleyden Atheneum Mechelen