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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{18}-a)(\frac{-13}{18}+x)& =(\color{red}{-a}+\color{orange}{\frac{13}{18}}).(\color{green}{x}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{13}{18})} . \color{green}{(x)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{18}a+\frac{13}{18}x-\frac{13}{18}.\frac{13}{18}& \text{Uitwerken } \\ & =-ax+\frac{13}{18}a+\frac{13}{18}x-\frac{169}{324} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{20}{8})(\frac{20}{16}-p)& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{-p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{4}a-\frac{5}{2}p+\frac{5}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =-ap+\frac{5}{4}a-\frac{5}{2}p+\frac{25}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-5}{18})(b+13)& =(\color{red}{b}+\color{orange}{\frac{5}{18}}).(\color{green}{b}+\color{blue}{13})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(13)} + \color{orange}{(\frac{5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = bb+13b+\frac{5}{18}b+\frac{5}{18}.13& \text{Uitwerken } \\ & =b^2+(13+\frac{5}{18})b+\frac{65}{18} & \text{Neem samen} \\ &=b^2+\frac{239}{18}b+\frac{65}{18} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-10}{8})(q+\frac{5}{7})& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{7}q+\frac{5}{4}q+\frac{5}{4}.\frac{5}{7}& \text{Uitwerken } \\ & =q^2+(\frac{5}{7}+\frac{5}{4})q+\frac{25}{28} & \text{Neem samen} \\ &=q^2+\frac{55}{28}q+\frac{25}{28} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{13}{12})(b+\frac{-7}{16})& =(\color{red}{a}+\color{orange}{\frac{-13}{12}}).(\color{green}{b}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{16}a-\frac{13}{12}b+\frac{13}{12}.\frac{7}{16}& \text{Uitwerken } \\ & =ab-\frac{7}{16}a-\frac{13}{12}b+\frac{91}{192} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{12}{10})(b+\frac{2}{17})& =(\color{red}{x}+\color{orange}{\frac{6}{5}}).(\color{green}{b}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{17}x+\frac{6}{5}b+\frac{6}{5}.\frac{2}{17}& \text{Uitwerken } \\ & =bx+\frac{2}{17}x+\frac{6}{5}b+\frac{12}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{18}+p)(\frac{9}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{9}}).(\color{green}{-q}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{20}p+\frac{1}{9}q-\frac{1}{9}.\frac{9}{20}& \text{Uitwerken } \\ & =-pq+\frac{9}{20}p+\frac{1}{9}q-\frac{9}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{9}{20}p+\frac{1}{9}q-\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{17}-p)(x-\frac{9}{17})& =(\color{red}{-p}+\color{orange}{\frac{15}{17}}).(\color{green}{x}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{15}{17})} . \color{green}{(x)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{17}p+\frac{15}{17}x-\frac{15}{17}.\frac{9}{17}& \text{Uitwerken } \\ & =-px+\frac{9}{17}p+\frac{15}{17}x-\frac{135}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-3}{18})(\frac{6}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ab+3a+\frac{1}{6}b+\frac{1}{6}.3& \text{Uitwerken } \\ & =ab+3a+\frac{1}{6}b+\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+3a+\frac{1}{6}b+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-7}{3})(\frac{-4}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{q}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{17}p-\frac{7}{3}q+\frac{7}{3}.\frac{4}{17}& \text{Uitwerken } \\ & =pq-\frac{4}{17}p-\frac{7}{3}q+\frac{28}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-20}{18})(b+\frac{11}{4})& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{b}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{4}x-\frac{10}{9}b-\frac{10}{9}.\frac{11}{4}& \text{Uitwerken } \\ & =bx+\frac{11}{4}x-\frac{10}{9}b-\frac{110}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{4}x-\frac{10}{9}b-\frac{55}{18} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{10}+b)(x+\frac{-19}{18})& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{18}b-\frac{1}{5}x+\frac{1}{5}.\frac{19}{18}& \text{Uitwerken } \\ & =bx-\frac{19}{18}b-\frac{1}{5}x+\frac{19}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-10 09:38:46
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