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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{19}{18})(\frac{-8}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{19}{18}}).(\color{green}{-p}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{19}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{13}q-\frac{19}{18}p-\frac{19}{18}.\frac{8}{13}& \text{Uitwerken } \\ & =-pq-\frac{8}{13}q-\frac{19}{18}p-\frac{152}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{8}{13}q-\frac{19}{18}p-\frac{76}{117} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{16}+x)(q-\frac{-12}{14})& =(\color{red}{x}+\color{orange}{\frac{-13}{16}}).(\color{green}{q}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{7}x-\frac{13}{16}q-\frac{13}{16}.\frac{6}{7}& \text{Uitwerken } \\ & =qx+\frac{6}{7}x-\frac{13}{16}q-\frac{78}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{6}{7}x-\frac{13}{16}q-\frac{39}{56} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-9}{6})(\frac{-15}{17}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{15}{17}x+\frac{3}{2}x-\frac{3}{2}.\frac{15}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-15}{17})+\frac{3}{2})x-(\frac{-45}{34}) & \text{Neem samen} \\ &=x^2+\frac{21}{34}x-(\frac{-45}{34}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{15}+p)(\frac{14}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{-b}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{14}{17}p+\frac{1}{5}b-\frac{1}{5}.\frac{14}{17}& \text{Uitwerken } \\ & =-bp+\frac{14}{17}p+\frac{1}{5}b-\frac{14}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{4}{4})(\frac{-7}{2}-b)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{2}q+1b+1.\frac{7}{2}& \text{Uitwerken } \\ & =-bq-\frac{7}{2}q+1b+\frac{7}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{14}+q)(\frac{-18}{11}+x)& =(\color{red}{q}+\color{orange}{\frac{10}{7}}).(\color{green}{x}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{18}{11}q+\frac{10}{7}x-\frac{10}{7}.\frac{18}{11}& \text{Uitwerken } \\ & =qx-\frac{18}{11}q+\frac{10}{7}x-\frac{180}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{4}{10})(a-\frac{-12}{3})& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aa+4a+\frac{2}{5}a+\frac{2}{5}.4& \text{Uitwerken } \\ & =a^2+(4+\frac{2}{5})a+\frac{8}{5} & \text{Neem samen} \\ &=a^2+\frac{22}{5}a+\frac{8}{5} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a-\frac{19}{12})(\frac{-10}{14}+a)& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{a}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{7}a-\frac{19}{12}a+\frac{19}{12}.\frac{5}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{7})+(\frac{-19}{12}))a+\frac{95}{84} & \text{Neem samen} \\ &=a^2-\frac{193}{84}a+\frac{95}{84} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(q+3)(\frac{13}{19}-x)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{-x}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(3)} . \color{green}{(-x)} + \color{orange}{(3)} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{19}q-3x+3.\frac{13}{19}& \text{Uitwerken } \\ & =-qx+\frac{13}{19}q-3x+\frac{39}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{10}{16})(a-\frac{-1}{14})& =(\color{red}{x}+\color{orange}{\frac{-5}{8}}).(\color{green}{a}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{14}x-\frac{5}{8}a-\frac{5}{8}.\frac{1}{14}& \text{Uitwerken } \\ & =ax+\frac{1}{14}x-\frac{5}{8}a-\frac{5}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{4}-b)(a-\frac{8}{14})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{4}{7}b-1a+1.\frac{4}{7}& \text{Uitwerken } \\ & =-ab+\frac{4}{7}b-1a+\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-6}{2})(q+\frac{-20}{19})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{19}b+3q-3.\frac{20}{19}& \text{Uitwerken } \\ & =bq-\frac{20}{19}b+3q-\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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