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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-14}{14})(b-\frac{-12}{16})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{4}b-1b-1.\frac{3}{4}& \text{Uitwerken } \\ & =b^2+(\frac{3}{4}+(-1))b-(\frac{-3}{4}) & \text{Neem samen} \\ &=b^2-\frac{1}{4}b-(\frac{-3}{4}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-11}{8})(\frac{15}{10}+b)& =(\color{red}{b}+\color{orange}{\frac{11}{8}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{2}b+\frac{11}{8}b+\frac{11}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+(\frac{3}{2}+\frac{11}{8})b+\frac{33}{16} & \text{Neem samen} \\ &=b^2+\frac{23}{8}b+\frac{33}{16} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{15}+a)(x+\frac{-1}{2})& =(\color{red}{a}+\color{orange}{\frac{11}{15}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{11}{15})} . \color{green}{(x)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a+\frac{11}{15}x-\frac{11}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a+\frac{11}{15}x-\frac{11}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{11}{15})(a-\frac{18}{5})& =(\color{red}{b}+\color{orange}{\frac{11}{15}}).(\color{green}{a}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{11}{15})} . \color{green}{(a)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{18}{5}b+\frac{11}{15}a-\frac{11}{15}.\frac{18}{5}& \text{Uitwerken } \\ & =ab-\frac{18}{5}b+\frac{11}{15}a-\frac{198}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{18}{5}b+\frac{11}{15}a-\frac{66}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{16}-x)(\frac{-9}{3}-b)& =(\color{red}{-x}+\color{orange}{\frac{1}{4}}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx+3x-\frac{1}{4}b-\frac{1}{4}.3& \text{Uitwerken } \\ & =bx+3x-\frac{1}{4}b-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{15}{14}+a)(b+\frac{3}{10})& =(\color{red}{a}+\color{orange}{\frac{15}{14}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{15}{14})} . \color{green}{(b)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{10}a+\frac{15}{14}b+\frac{15}{14}.\frac{3}{10}& \text{Uitwerken } \\ & =ab+\frac{3}{10}a+\frac{15}{14}b+\frac{45}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{10}a+\frac{15}{14}b+\frac{9}{28} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{14}+x)(\frac{18}{9}-p)& =(\color{red}{x}+\color{orange}{\frac{13}{14}}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{13}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -px+2x-\frac{13}{14}p+\frac{13}{14}.2& \text{Uitwerken } \\ & =-px+2x-\frac{13}{14}p+\frac{26}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+2x-\frac{13}{14}p+\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-3}{18})(\frac{-8}{15}-x)& =(\color{red}{b}+\color{orange}{\frac{1}{6}}).(\color{green}{-x}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{1}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{15}b-\frac{1}{6}x-\frac{1}{6}.\frac{8}{15}& \text{Uitwerken } \\ & =-bx-\frac{8}{15}b-\frac{1}{6}x-\frac{8}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{8}{15}b-\frac{1}{6}x-\frac{4}{45} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{8}+q)(\frac{-7}{12}-x)& =(\color{red}{q}+\color{orange}{\frac{5}{8}}).(\color{green}{-x}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{5}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{12}q-\frac{5}{8}x-\frac{5}{8}.\frac{7}{12}& \text{Uitwerken } \\ & =-qx-\frac{7}{12}q-\frac{5}{8}x-\frac{35}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{18}{7})(\frac{-10}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{18}{7}}).(\color{green}{-p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{18}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{2}a-\frac{18}{7}p-\frac{18}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =-ap-\frac{5}{2}a-\frac{18}{7}p-\frac{90}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{5}{2}a-\frac{18}{7}p-\frac{45}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{15}+q)(\frac{16}{12}-a)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{-a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{3}q+\frac{3}{5}a-\frac{3}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =-aq+\frac{4}{3}q+\frac{3}{5}a-\frac{12}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{4}{3}q+\frac{3}{5}a-\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{17}-q)(\frac{-5}{2}-a)& =(\color{red}{-q}+\color{orange}{\frac{-5}{17}}).(\color{green}{-a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{2}q+\frac{5}{17}a+\frac{5}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =aq+\frac{5}{2}q+\frac{5}{17}a+\frac{25}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-20 15:16:44
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