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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{6}{5}-a)(\frac{10}{16}+a)& =(\color{red}{-a}+\color{orange}{\frac{6}{5}}).(\color{green}{a}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{8}a+\frac{6}{5}a+\frac{6}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{8})+\frac{6}{5})a+(\frac{-30}{40}) & \text{Neem samen} \\ &=-a^2+\frac{23}{40}a+(\frac{-30}{40}) & \text{Maak de som} \\ &=-a^2+\frac{23}{40}a+(\frac{-3}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{3}-x)(b+\frac{3}{7})& =(\color{red}{-x}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{7}x-\frac{2}{3}b-\frac{2}{3}.\frac{3}{7}& \text{Uitwerken } \\ & =-bx-\frac{3}{7}x-\frac{2}{3}b-\frac{6}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{3}{7}x-\frac{2}{3}b-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{13}+q)(\frac{-13}{7}-p)& =(\color{red}{q}+\color{orange}{\frac{11}{13}}).(\color{green}{-p}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{11}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{7}q-\frac{11}{13}p-\frac{11}{13}.\frac{13}{7}& \text{Uitwerken } \\ & =-pq-\frac{13}{7}q-\frac{11}{13}p-\frac{143}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{13}{7}q-\frac{11}{13}p-\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{20}{14})(x-\frac{-10}{20})& =(\color{red}{q}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}q-\frac{10}{7}x-\frac{10}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}q-\frac{10}{7}x-\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{2}q-\frac{10}{7}x-\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{12}-p)(x-\frac{-13}{11})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{11}p+1x+1.\frac{13}{11}& \text{Uitwerken } \\ & =-px-\frac{13}{11}p+1x+\frac{13}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{10}{18})(p+(-6))& =(\color{red}{x}+\color{orange}{\frac{-5}{9}}).(\color{green}{p}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-6)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = px-6x-\frac{5}{9}p+\frac{5}{9}.6& \text{Uitwerken } \\ & =px-6x-\frac{5}{9}p+\frac{30}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-6x-\frac{5}{9}p+\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{11}+q)(p+\frac{-7}{11})& =(\color{red}{q}+\color{orange}{\frac{3}{11}}).(\color{green}{p}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{11}q+\frac{3}{11}p-\frac{3}{11}.\frac{7}{11}& \text{Uitwerken } \\ & =pq-\frac{7}{11}q+\frac{3}{11}p-\frac{21}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{17}+p)(\frac{-5}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{9}{17}}).(\color{green}{-x}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{9}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{16}p-\frac{9}{17}x-\frac{9}{17}.\frac{5}{16}& \text{Uitwerken } \\ & =-px-\frac{5}{16}p-\frac{9}{17}x-\frac{45}{272} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-13}{3})(\frac{-6}{12}+p)& =(\color{red}{a}+\color{orange}{\frac{-13}{3}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{2}a-\frac{13}{3}p+\frac{13}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =ap-\frac{1}{2}a-\frac{13}{3}p+\frac{13}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{3}{6})(\frac{10}{4}+a)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{2}b-\frac{1}{2}a-\frac{1}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =ab+\frac{5}{2}b-\frac{1}{2}a-\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{14}+b)(\frac{-1}{15}+q)& =(\color{red}{b}+\color{orange}{\frac{-11}{14}}).(\color{green}{q}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{15}b-\frac{11}{14}q+\frac{11}{14}.\frac{1}{15}& \text{Uitwerken } \\ & =bq-\frac{1}{15}b-\frac{11}{14}q+\frac{11}{210} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{18}+b)(\frac{3}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{2}b+\frac{2}{3}a+\frac{2}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =ab+\frac{3}{2}b+\frac{2}{3}a+\frac{6}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{2}b+\frac{2}{3}a+1 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-19 23:02:56
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