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

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  1. \((\frac{4}{20}+p)(\frac{15}{19}-p)\)
  2. \((a-\frac{2}{10})(a+\frac{-14}{10})\)
  3. \((\frac{-15}{13}+p)(p+\frac{1}{14})\)
  4. \((\frac{-18}{7}+a)(b+\frac{-17}{11})\)
  5. \((\frac{-10}{11}-b)(\frac{12}{14}+q)\)
  6. \((a-\frac{1}{7})(a+\frac{3}{20})\)
  7. \((\frac{-5}{15}-a)(q+(-19))\)
  8. \((\frac{12}{3}-x)(\frac{-20}{18}-q)\)
  9. \((\frac{-12}{5}+x)(\frac{-1}{6}+x)\)
  10. \((\frac{-11}{5}-a)(q+\frac{-2}{10})\)
  11. \((\frac{-9}{15}+a)(\frac{15}{2}-p)\)
  12. \((a+\frac{-16}{18})(b+\frac{-6}{16})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{20}+p)(\frac{15}{19}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{-p}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{15}{19}p-\frac{1}{5}p+\frac{1}{5}.\frac{15}{19}& \text{Uitwerken } \\ & =-p^2+(\frac{15}{19}+(\frac{-1}{5}))p+(\frac{-15}{95}) & \text{Neem samen} \\ &=-p^2+\frac{56}{95}p+(\frac{-15}{95}) & \text{Maak de som} \\ &=-p^2+\frac{56}{95}p+(\frac{-3}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(a-\frac{2}{10})(a+\frac{-14}{10})& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{5}a-\frac{1}{5}a+\frac{1}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{5})+(\frac{-1}{5}))a+\frac{7}{25} & \text{Neem samen} \\ &=a^2-\frac{8}{5}a+\frac{7}{25} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{13}+p)(p+\frac{1}{14})& =(\color{red}{p}+\color{orange}{\frac{-15}{13}}).(\color{green}{p}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{14}p-\frac{15}{13}p-\frac{15}{13}.\frac{1}{14}& \text{Uitwerken } \\ & =p^2+(\frac{1}{14}+(\frac{-15}{13}))p-(\frac{-15}{182}) & \text{Neem samen} \\ &=p^2-\frac{197}{182}p-(\frac{-15}{182}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{7}+a)(b+\frac{-17}{11})& =(\color{red}{a}+\color{orange}{\frac{-18}{7}}).(\color{green}{b}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{11}a-\frac{18}{7}b+\frac{18}{7}.\frac{17}{11}& \text{Uitwerken } \\ & =ab-\frac{17}{11}a-\frac{18}{7}b+\frac{306}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{11}-b)(\frac{12}{14}+q)& =(\color{red}{-b}+\color{orange}{\frac{-10}{11}}).(\color{green}{q}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{7}b-\frac{10}{11}q-\frac{10}{11}.\frac{6}{7}& \text{Uitwerken } \\ & =-bq-\frac{6}{7}b-\frac{10}{11}q-\frac{60}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{1}{7})(a+\frac{3}{20})& =(\color{red}{a}+\color{orange}{\frac{-1}{7}}).(\color{green}{a}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{20}a-\frac{1}{7}a-\frac{1}{7}.\frac{3}{20}& \text{Uitwerken } \\ & =a^2+(\frac{3}{20}+(\frac{-1}{7}))a-(\frac{-3}{140}) & \text{Neem samen} \\ &=a^2+\frac{1}{140}a-(\frac{-3}{140}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-5}{15}-a)(q+(-19))& =(\color{red}{-a}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{(-19)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-19)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -aq+19a-\frac{1}{3}q+\frac{1}{3}.19& \text{Uitwerken } \\ & =-aq+19a-\frac{1}{3}q+\frac{19}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{3}-x)(\frac{-20}{18}-q)& =(\color{red}{-x}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{10}{9}x-4q-4.\frac{10}{9}& \text{Uitwerken } \\ & =qx+\frac{10}{9}x-4q-\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-12}{5}+x)(\frac{-1}{6}+x)& =(\color{red}{x}+\color{orange}{\frac{-12}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{6}x-\frac{12}{5}x+\frac{12}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{6})+(\frac{-12}{5}))x+\frac{12}{30} & \text{Neem samen} \\ &=x^2-\frac{77}{30}x+\frac{12}{30} & \text{Maak de som} \\ &=x^2-\frac{77}{30}x+\frac{2}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{5}-a)(q+\frac{-2}{10})& =(\color{red}{-a}+\color{orange}{\frac{-11}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{5}a-\frac{11}{5}q+\frac{11}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =-aq+\frac{1}{5}a-\frac{11}{5}q+\frac{11}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{15}+a)(\frac{15}{2}-p)& =(\color{red}{a}+\color{orange}{\frac{-3}{5}}).(\color{green}{-p}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{15}{2}a+\frac{3}{5}p-\frac{3}{5}.\frac{15}{2}& \text{Uitwerken } \\ & =-ap+\frac{15}{2}a+\frac{3}{5}p-\frac{45}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{15}{2}a+\frac{3}{5}p-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-16}{18})(b+\frac{-6}{16})& =(\color{red}{a}+\color{orange}{\frac{-8}{9}}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{8}a-\frac{8}{9}b+\frac{8}{9}.\frac{3}{8}& \text{Uitwerken } \\ & =ab-\frac{3}{8}a-\frac{8}{9}b+\frac{24}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{8}a-\frac{8}{9}b+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
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