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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{3}+a)(\frac{-7}{13}+q)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{13}a-6q+6.\frac{7}{13}& \text{Uitwerken } \\ & =aq-\frac{7}{13}a-6q+\frac{42}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{7}+p)(b+\frac{-13}{13})& =(\color{red}{p}+\color{orange}{\frac{-8}{7}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p-\frac{8}{7}b+\frac{8}{7}.1& \text{Uitwerken } \\ & =bp-1p-\frac{8}{7}b+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{8}{20})(q-\frac{11}{4})& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{4}b-\frac{2}{5}q+\frac{2}{5}.\frac{11}{4}& \text{Uitwerken } \\ & =bq-\frac{11}{4}b-\frac{2}{5}q+\frac{22}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{11}{4}b-\frac{2}{5}q+\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{3}{13})(\frac{14}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{3}{13}}).(\color{green}{-x}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{3}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{14}{9}x-\frac{3}{13}x+\frac{3}{13}.\frac{14}{9}& \text{Uitwerken } \\ & =-x^2+(\frac{14}{9}+(\frac{-3}{13}))x+(\frac{-42}{117}) & \text{Neem samen} \\ &=-x^2+\frac{155}{117}x+(\frac{-42}{117}) & \text{Maak de som} \\ &=-x^2+\frac{155}{117}x+(\frac{-14}{39}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(q+\frac{13}{18})((-14)+p)& =(\color{red}{q}+\color{orange}{\frac{13}{18}}).(\color{green}{p}+\color{blue}{(-14)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-14)} + \color{orange}{(\frac{13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = pq-14q+\frac{13}{18}p-\frac{13}{18}.14& \text{Uitwerken } \\ & =pq-14q+\frac{13}{18}p-\frac{182}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-14q+\frac{13}{18}p-\frac{91}{9} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{10}{7})(p-\frac{-13}{20})& =(\color{red}{b}+\color{orange}{\frac{-10}{7}}).(\color{green}{p}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{20}b-\frac{10}{7}p-\frac{10}{7}.\frac{13}{20}& \text{Uitwerken } \\ & =bp+\frac{13}{20}b-\frac{10}{7}p-\frac{130}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{20}b-\frac{10}{7}p-\frac{13}{14} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+7)(q+(-20))& =(\color{red}{p}+\color{orange}{7}).(\color{green}{q}+\color{blue}{(-20)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-20)} + \color{orange}{(7)} . \color{green}{(q)} + \color{orange}{(7)} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = pq-20p+7q-7.20& \text{Uitwerken } \\ & =pq-20p+7q-140 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{7}-p)(x-\frac{-4}{18})& =(\color{red}{-p}+\color{orange}{\frac{18}{7}}).(\color{green}{x}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{18}{7})} . \color{green}{(x)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{9}p+\frac{18}{7}x+\frac{18}{7}.\frac{2}{9}& \text{Uitwerken } \\ & =-px-\frac{2}{9}p+\frac{18}{7}x+\frac{36}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{2}{9}p+\frac{18}{7}x+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{13}{13}-a)(p+\frac{10}{2})& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(5)} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ap-5a+1p+1.5& \text{Uitwerken } \\ & =-ap-5a+1p+5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-5}{17})(b+\frac{-16}{9})& =(\color{red}{q}+\color{orange}{\frac{-5}{17}}).(\color{green}{b}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{9}q-\frac{5}{17}b+\frac{5}{17}.\frac{16}{9}& \text{Uitwerken } \\ & =bq-\frac{16}{9}q-\frac{5}{17}b+\frac{80}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{15}-a)(\frac{4}{14}-q)& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{-q}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{7}a+\frac{4}{3}q-\frac{4}{3}.\frac{2}{7}& \text{Uitwerken } \\ & =aq-\frac{2}{7}a+\frac{4}{3}q-\frac{8}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-13}{4})(q+\frac{-5}{13})& =(\color{red}{q}+\color{orange}{\frac{-13}{4}}).(\color{green}{q}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{13}q-\frac{13}{4}q+\frac{13}{4}.\frac{5}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{13})+(\frac{-13}{4}))q+\frac{65}{52} & \text{Neem samen} \\ &=q^2-\frac{189}{52}q+\frac{65}{52} & \text{Maak de som} \\ &=q^2-\frac{189}{52}q+\frac{5}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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