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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{17}+q)(\frac{6}{18}+b)& =(\color{red}{q}+\color{orange}{\frac{9}{17}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{9}{17})} . \color{green}{(b)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}q+\frac{9}{17}b+\frac{9}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}q+\frac{9}{17}b+\frac{9}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{3}q+\frac{9}{17}b+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-7}{16}+b)(\frac{11}{15}+q)& =(\color{red}{b}+\color{orange}{\frac{-7}{16}}).(\color{green}{q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{15}b-\frac{7}{16}q-\frac{7}{16}.\frac{11}{15}& \text{Uitwerken } \\ & =bq+\frac{11}{15}b-\frac{7}{16}q-\frac{77}{240} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-8}{4})(\frac{-14}{8}-q)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{4}x+2q+2.\frac{7}{4}& \text{Uitwerken } \\ & =-qx-\frac{7}{4}x+2q+\frac{14}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{7}{4}x+2q+\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{9}+x)(a-\frac{-7}{2})& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{2}x-\frac{10}{9}a-\frac{10}{9}.\frac{7}{2}& \text{Uitwerken } \\ & =ax+\frac{7}{2}x-\frac{10}{9}a-\frac{70}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{2}x-\frac{10}{9}a-\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{10}+b)(a+\frac{3}{8})& =(\color{red}{b}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{8}b-\frac{3}{5}a-\frac{3}{5}.\frac{3}{8}& \text{Uitwerken } \\ & =ab+\frac{3}{8}b-\frac{3}{5}a-\frac{9}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-15}{15})(q-\frac{2}{10})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{5}b-1q+1.\frac{1}{5}& \text{Uitwerken } \\ & =bq-\frac{1}{5}b-1q+\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{9}{18})(p-\frac{-5}{3})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{3}q+\frac{1}{2}p+\frac{1}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =pq+\frac{5}{3}q+\frac{1}{2}p+\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+(-9))(\frac{1}{16}-x)& =(\color{red}{a}+\color{orange}{(-9)}).(\color{green}{-x}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(-9)} . \color{green}{(-x)} + \color{orange}{(-9)} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{16}a+9x-9.\frac{1}{16}& \text{Uitwerken } \\ & =-ax+\frac{1}{16}a+9x-\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-3)+q)(q+\frac{5}{6})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{6}q-3q-3.\frac{5}{6}& \text{Uitwerken } \\ & =q^2+(\frac{5}{6}+(-3))q-(\frac{-15}{6}) & \text{Neem samen} \\ &=q^2-\frac{13}{6}q-(\frac{-15}{6}) & \text{Maak de som} \\ &=q^2-\frac{13}{6}q+\frac{5}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{7}-x)(p+\frac{13}{5})& =(\color{red}{-x}+\color{orange}{\frac{1}{7}}).(\color{green}{p}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{1}{7})} . \color{green}{(p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{5}x+\frac{1}{7}p+\frac{1}{7}.\frac{13}{5}& \text{Uitwerken } \\ & =-px-\frac{13}{5}x+\frac{1}{7}p+\frac{13}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-(-5))(a+\frac{16}{9})& =(\color{red}{a}+\color{orange}{5}).(\color{green}{a}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(5)} . \color{green}{(a)} + \color{orange}{(5)} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{16}{9}a+5a+5.\frac{16}{9}& \text{Uitwerken } \\ & =a^2+(\frac{16}{9}+5)a+\frac{80}{9} & \text{Neem samen} \\ &=a^2+\frac{61}{9}a+\frac{80}{9} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{18}-b)(\frac{-4}{6}+p)& =(\color{red}{-b}+\color{orange}{\frac{13}{18}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{3}b+\frac{13}{18}p-\frac{13}{18}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp+\frac{2}{3}b+\frac{13}{18}p-\frac{26}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{2}{3}b+\frac{13}{18}p-\frac{13}{27} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-03 07:34:15
Een site van Busleyden Atheneum Mechelen