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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{14}{8}-a)(q+\frac{6}{3})& =(\color{red}{-a}+\color{orange}{\frac{7}{4}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2a+\frac{7}{4}q+\frac{7}{4}.2& \text{Uitwerken } \\ & =-aq-2a+\frac{7}{4}q+\frac{14}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-2a+\frac{7}{4}q+\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-6}{15})(\frac{20}{10}-a)& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap+2p-\frac{2}{5}a+\frac{2}{5}.2& \text{Uitwerken } \\ & =-ap+2p-\frac{2}{5}a+\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-14}{9})(b+\frac{20}{5})& =(\color{red}{a}+\color{orange}{\frac{14}{9}}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{14}{9})} . \color{green}{(b)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ab+4a+\frac{14}{9}b+\frac{14}{9}.4& \text{Uitwerken } \\ & =ab+4a+\frac{14}{9}b+\frac{56}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{10}{8})(\frac{-6}{11}+p)& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{p}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{11}x-\frac{5}{4}p+\frac{5}{4}.\frac{6}{11}& \text{Uitwerken } \\ & =px-\frac{6}{11}x-\frac{5}{4}p+\frac{30}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{6}{11}x-\frac{5}{4}p+\frac{15}{22} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{17}{17}+b)(p+\frac{-1}{9})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{9}b+1p-1.\frac{1}{9}& \text{Uitwerken } \\ & =bp-\frac{1}{9}b+1p-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{13}+p)(4-x)& =(\color{red}{p}+\color{orange}{\frac{-4}{13}}).(\color{green}{-x}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{-4}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -px+4p+\frac{4}{13}x-\frac{4}{13}.4& \text{Uitwerken } \\ & =-px+4p+\frac{4}{13}x-\frac{16}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-12}{16})(\frac{5}{8}+b)& =(\color{red}{b}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{8}b+\frac{3}{4}b+\frac{3}{4}.\frac{5}{8}& \text{Uitwerken } \\ & =b^2+(\frac{5}{8}+\frac{3}{4})b+\frac{15}{32} & \text{Neem samen} \\ &=b^2+\frac{11}{8}b+\frac{15}{32} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-4}{3})(p-\frac{-18}{5})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{5}q+\frac{4}{3}p+\frac{4}{3}.\frac{18}{5}& \text{Uitwerken } \\ & =pq+\frac{18}{5}q+\frac{4}{3}p+\frac{72}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{18}{5}q+\frac{4}{3}p+\frac{24}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-18}{2})(b-\frac{11}{14})& =(\color{red}{q}+\color{orange}{9}).(\color{green}{b}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(9)} . \color{green}{(b)} + \color{orange}{(9)} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{14}q+9b-9.\frac{11}{14}& \text{Uitwerken } \\ & =bq-\frac{11}{14}q+9b-\frac{99}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-20}{20})(\frac{2}{7}-p)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{7}x+1p-1.\frac{2}{7}& \text{Uitwerken } \\ & =-px+\frac{2}{7}x+1p-\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-10}{5}+x)(x+\frac{-13}{3})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{13}{3}x-2x+2.\frac{13}{3}& \text{Uitwerken } \\ & =x^2+((\frac{-13}{3})+(-2))x+\frac{26}{3} & \text{Neem samen} \\ &=x^2-\frac{19}{3}x+\frac{26}{3} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b+\frac{6}{14})(p-\frac{20}{4})& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bp-5b+\frac{3}{7}p-\frac{3}{7}.5& \text{Uitwerken } \\ & =bp-5b+\frac{3}{7}p-\frac{15}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-13 09:56:52
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