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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-7}{5}+x)(\frac{11}{2}+x)& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{11}{2}x-\frac{7}{5}x-\frac{7}{5}.\frac{11}{2}& \text{Uitwerken } \\ & =x^2+(\frac{11}{2}+(\frac{-7}{5}))x-(\frac{-77}{10}) & \text{Neem samen} \\ &=x^2+\frac{41}{10}x-(\frac{-77}{10}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(10-x)(\frac{9}{9}-b)& =(\color{red}{-x}+\color{orange}{10}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(10)} . \color{green}{(-b)} + \color{orange}{(10)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx-1x-10b+10.1& \text{Uitwerken } \\ & =bx-1x-10b+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{9}-x)(\frac{7}{9}-x)& =(\color{red}{-x}+\color{orange}{\frac{19}{9}}).(\color{green}{-x}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{19}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{9}x-\frac{19}{9}x+\frac{19}{9}.\frac{7}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{9})+(\frac{-19}{9}))x+\frac{133}{81} & \text{Neem samen} \\ &=x^2-\frac{26}{9}x+\frac{133}{81} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-1}{8}-b)(\frac{-9}{6}+x)& =(\color{red}{-b}+\color{orange}{\frac{-1}{8}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{2}b-\frac{1}{8}x+\frac{1}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =-bx+\frac{3}{2}b-\frac{1}{8}x+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{8}+b)(q+\frac{18}{7})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{7}b-\frac{1}{2}q-\frac{1}{2}.\frac{18}{7}& \text{Uitwerken } \\ & =bq+\frac{18}{7}b-\frac{1}{2}q-\frac{18}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{7}b-\frac{1}{2}q-\frac{9}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{2}{13})(p+(-16))& =(\color{red}{p}+\color{orange}{\frac{-2}{13}}).(\color{green}{p}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-16)} + \color{orange}{(\frac{-2}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = pp-16p-\frac{2}{13}p+\frac{2}{13}.16& \text{Uitwerken } \\ & =p^2+((-16)+(\frac{-2}{13}))p+\frac{32}{13} & \text{Neem samen} \\ &=p^2-\frac{210}{13}p+\frac{32}{13} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q+\frac{1}{14})(\frac{17}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{1}{14})} . \color{green}{(a)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{20}q+\frac{1}{14}a+\frac{1}{14}.\frac{17}{20}& \text{Uitwerken } \\ & =aq+\frac{17}{20}q+\frac{1}{14}a+\frac{17}{280} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-3}{18})(\frac{-16}{20}-b)& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{-b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{5}a+\frac{1}{6}b+\frac{1}{6}.\frac{4}{5}& \text{Uitwerken } \\ & =-ab-\frac{4}{5}a+\frac{1}{6}b+\frac{4}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{4}{5}a+\frac{1}{6}b+\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-11}{20})(\frac{-16}{18}+x)& =(\color{red}{x}+\color{orange}{\frac{-11}{20}}).(\color{green}{x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{8}{9}x-\frac{11}{20}x+\frac{11}{20}.\frac{8}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-8}{9})+(\frac{-11}{20}))x+\frac{88}{180} & \text{Neem samen} \\ &=x^2-\frac{259}{180}x+\frac{88}{180} & \text{Maak de som} \\ &=x^2-\frac{259}{180}x+\frac{22}{45} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-20}{19})(b-\frac{-17}{15})& =(\color{red}{q}+\color{orange}{\frac{-20}{19}}).(\color{green}{b}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{15}q-\frac{20}{19}b-\frac{20}{19}.\frac{17}{15}& \text{Uitwerken } \\ & =bq+\frac{17}{15}q-\frac{20}{19}b-\frac{340}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{15}q-\frac{20}{19}b-\frac{68}{57} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p-\frac{15}{3})(\frac{-2}{17}+a)& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{a}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(-5)} . \color{green}{(a)} + \color{orange}{(-5)} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{17}p-5a+5.\frac{2}{17}& \text{Uitwerken } \\ & =ap-\frac{2}{17}p-5a+\frac{10}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{14}+p)(b-\frac{5}{13})& =(\color{red}{p}+\color{orange}{\frac{-10}{7}}).(\color{green}{b}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{13}p-\frac{10}{7}b+\frac{10}{7}.\frac{5}{13}& \text{Uitwerken } \\ & =bp-\frac{5}{13}p-\frac{10}{7}b+\frac{50}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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