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

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  1. \((\frac{13}{13}+p)(b-\frac{12}{14})\)
  2. \((\frac{12}{5}+a)(\frac{-5}{13}+x)\)
  3. \((q-\frac{-4}{7})(q+\frac{16}{7})\)
  4. \((q+\frac{12}{2})(q-\frac{18}{18})\)
  5. \((a-\frac{-12}{4})(\frac{11}{20}+b)\)
  6. \((p+\frac{-20}{3})(p+\frac{-9}{5})\)
  7. \((\frac{-19}{19}+b)(a-\frac{5}{20})\)
  8. \((b-\frac{-9}{10})(\frac{-17}{3}-q)\)
  9. \((\frac{-14}{5}-q)(\frac{-12}{8}-q)\)
  10. \((b+(-9))(\frac{-10}{20}-b)\)
  11. \((x+\frac{-6}{3})(a+\frac{-20}{2})\)
  12. \((x-\frac{-20}{12})(\frac{1}{4}+p)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{13}+p)(b-\frac{12}{14})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{7}p+1b-1.\frac{6}{7}& \text{Uitwerken } \\ & =bp-\frac{6}{7}p+1b-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{5}+a)(\frac{-5}{13}+x)& =(\color{red}{a}+\color{orange}{\frac{12}{5}}).(\color{green}{x}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{12}{5})} . \color{green}{(x)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{13}a+\frac{12}{5}x-\frac{12}{5}.\frac{5}{13}& \text{Uitwerken } \\ & =ax-\frac{5}{13}a+\frac{12}{5}x-\frac{60}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{13}a+\frac{12}{5}x-\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-4}{7})(q+\frac{16}{7})& =(\color{red}{q}+\color{orange}{\frac{4}{7}}).(\color{green}{q}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{16}{7}q+\frac{4}{7}q+\frac{4}{7}.\frac{16}{7}& \text{Uitwerken } \\ & =q^2+(\frac{16}{7}+\frac{4}{7})q+\frac{64}{49} & \text{Neem samen} \\ &=q^2+\frac{20}{7}q+\frac{64}{49} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(q+\frac{12}{2})(q-\frac{18}{18})& =(\color{red}{q}+\color{orange}{6}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qq-1q+6q-6.1& \text{Uitwerken } \\ & =q^2+((-1)+6)q-(-6) & \text{Neem samen} \\ &=q^2+5q-(-6) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-12}{4})(\frac{11}{20}+b)& =(\color{red}{a}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{20}a+3b+3.\frac{11}{20}& \text{Uitwerken } \\ & =ab+\frac{11}{20}a+3b+\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-20}{3})(p+\frac{-9}{5})& =(\color{red}{p}+\color{orange}{\frac{-20}{3}}).(\color{green}{p}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{9}{5}p-\frac{20}{3}p+\frac{20}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-9}{5})+(\frac{-20}{3}))p+\frac{180}{15} & \text{Neem samen} \\ &=p^2-\frac{127}{15}p+\frac{180}{15} & \text{Maak de som} \\ &=p^2-\frac{127}{15}p+12 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{19}+b)(a-\frac{5}{20})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{4}b-1a+1.\frac{1}{4}& \text{Uitwerken } \\ & =ab-\frac{1}{4}b-1a+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-9}{10})(\frac{-17}{3}-q)& =(\color{red}{b}+\color{orange}{\frac{9}{10}}).(\color{green}{-q}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{9}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{17}{3}b-\frac{9}{10}q-\frac{9}{10}.\frac{17}{3}& \text{Uitwerken } \\ & =-bq-\frac{17}{3}b-\frac{9}{10}q-\frac{153}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{17}{3}b-\frac{9}{10}q-\frac{51}{10} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{5}-q)(\frac{-12}{8}-q)& =(\color{red}{-q}+\color{orange}{\frac{-14}{5}}).(\color{green}{-q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{2}q+\frac{14}{5}q+\frac{14}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =q^2+(\frac{3}{2}+\frac{14}{5})q+\frac{42}{10} & \text{Neem samen} \\ &=q^2+\frac{43}{10}q+\frac{42}{10} & \text{Maak de som} \\ &=q^2+\frac{43}{10}q+\frac{21}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(b+(-9))(\frac{-10}{20}-b)& =(\color{red}{b}+\color{orange}{(-9)}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-9)} . \color{green}{(-b)} + \color{orange}{(-9)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{2}b+9b+9.\frac{1}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{2})+9)b+(\frac{-9}{2}) & \text{Neem samen} \\ &=-b^2+\frac{17}{2}b+(\frac{-9}{2}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-6}{3})(a+\frac{-20}{2})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-10)} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = ax-10x-2a+2.10& \text{Uitwerken } \\ & =ax-10x-2a+20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-20}{12})(\frac{1}{4}+p)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{4}x+\frac{5}{3}p+\frac{5}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =px+\frac{1}{4}x+\frac{5}{3}p+\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-09 21:19:21
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