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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{2}+x)(\frac{-1}{4}-q)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{4}x-2q-2.\frac{1}{4}& \text{Uitwerken } \\ & =-qx-\frac{1}{4}x-2q-\frac{2}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{1}{4}x-2q-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-2}{10})(a-\frac{-6}{16})& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{8}q+\frac{1}{5}a+\frac{1}{5}.\frac{3}{8}& \text{Uitwerken } \\ & =aq+\frac{3}{8}q+\frac{1}{5}a+\frac{3}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{9}+b)(x-\frac{9}{6})& =(\color{red}{b}+\color{orange}{\frac{16}{9}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{2}b+\frac{16}{9}x-\frac{16}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =bx-\frac{3}{2}b+\frac{16}{9}x-\frac{48}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{2}b+\frac{16}{9}x-\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{3}+x)(b+\frac{16}{11})& =(\color{red}{x}+\color{orange}{\frac{11}{3}}).(\color{green}{b}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{11}{3})} . \color{green}{(b)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{11}x+\frac{11}{3}b+\frac{11}{3}.\frac{16}{11}& \text{Uitwerken } \\ & =bx+\frac{16}{11}x+\frac{11}{3}b+\frac{176}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{16}{11}x+\frac{11}{3}b+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(12+q)(\frac{11}{17}-p)& =(\color{red}{q}+\color{orange}{12}).(\color{green}{-p}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(12)} . \color{green}{(-p)} + \color{orange}{(12)} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{17}q-12p+12.\frac{11}{17}& \text{Uitwerken } \\ & =-pq+\frac{11}{17}q-12p+\frac{132}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-7}{7})(\frac{3}{20}+x)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{20}p+1x+1.\frac{3}{20}& \text{Uitwerken } \\ & =px+\frac{3}{20}p+1x+\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{1}{20})(\frac{-8}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{1}{20}}).(\color{green}{-x}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{1}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{8}{15}a-\frac{1}{20}x-\frac{1}{20}.\frac{8}{15}& \text{Uitwerken } \\ & =-ax-\frac{8}{15}a-\frac{1}{20}x-\frac{8}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{8}{15}a-\frac{1}{20}x-\frac{2}{75} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{20}+a)(p+\frac{-12}{11})& =(\color{red}{a}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{12}{11}a-\frac{7}{10}p+\frac{7}{10}.\frac{12}{11}& \text{Uitwerken } \\ & =ap-\frac{12}{11}a-\frac{7}{10}p+\frac{84}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{12}{11}a-\frac{7}{10}p+\frac{42}{55} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}((-16)-q)(\frac{6}{8}-q)& =(\color{red}{-q}+\color{orange}{(-16)}).(\color{green}{-q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-16)} . \color{green}{(-q)} + \color{orange}{(-16)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{4}q+16q-16.\frac{3}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{4})+16)q-(\frac{-48}{4}) & \text{Neem samen} \\ &=q^2+\frac{61}{4}q-(\frac{-48}{4}) & \text{Maak de som} \\ &=q^2+\frac{61}{4}q+12 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{10}+a)(a+8)& =(\color{red}{a}+\color{orange}{\frac{8}{5}}).(\color{green}{a}+\color{blue}{8})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = aa+8a+\frac{8}{5}a+\frac{8}{5}.8& \text{Uitwerken } \\ & =a^2+(8+\frac{8}{5})a+\frac{64}{5} & \text{Neem samen} \\ &=a^2+\frac{48}{5}a+\frac{64}{5} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-17}{17})(\frac{-15}{6}-q)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{2}b-1q-1.\frac{5}{2}& \text{Uitwerken } \\ & =-bq-\frac{5}{2}b-1q-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{19}{14})(a-\frac{-5}{12})& =(\color{red}{x}+\color{orange}{\frac{19}{14}}).(\color{green}{a}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{12}x+\frac{19}{14}a+\frac{19}{14}.\frac{5}{12}& \text{Uitwerken } \\ & =ax+\frac{5}{12}x+\frac{19}{14}a+\frac{95}{168} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-09 13:50:51
Een site van Busleyden Atheneum Mechelen