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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{15}-p)(b-\frac{14}{12})& =(\color{red}{-p}+\color{orange}{\frac{-6}{5}}).(\color{green}{b}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{6}p-\frac{6}{5}b+\frac{6}{5}.\frac{7}{6}& \text{Uitwerken } \\ & =-bp+\frac{7}{6}p-\frac{6}{5}b+\frac{42}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{7}{6}p-\frac{6}{5}b+\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{15}-p)(b+\frac{-1}{4})& =(\color{red}{-p}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{4}p+\frac{4}{5}b-\frac{4}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =-bp+\frac{1}{4}p+\frac{4}{5}b-\frac{4}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{4}p+\frac{4}{5}b-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{3}{5})(\frac{-11}{2}+b)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{2}q-\frac{3}{5}b+\frac{3}{5}.\frac{11}{2}& \text{Uitwerken } \\ & =bq-\frac{11}{2}q-\frac{3}{5}b+\frac{33}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{7}{8})(\frac{8}{8}-q)& =(\color{red}{q}+\color{orange}{\frac{7}{8}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qq+1q-\frac{7}{8}q+\frac{7}{8}.1& \text{Uitwerken } \\ & =-q^2+(1+(\frac{-7}{8}))q+(\frac{-7}{8}) & \text{Neem samen} \\ &=-q^2+\frac{1}{8}q+(\frac{-7}{8}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x-(-10))(x-\frac{-4}{2})& =(\color{red}{x}+\color{orange}{10}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(10)} . \color{green}{(x)} + \color{orange}{(10)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x+10x+10.2& \text{Uitwerken } \\ & =x^2+(2+10)x+20 & \text{Neem samen} \\ &=x^2+12x+20 & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-10}{2})(p+\frac{15}{10})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{2}x+5p+5.\frac{3}{2}& \text{Uitwerken } \\ & =px+\frac{3}{2}x+5p+\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{18}-p)(b+\frac{-8}{10})& =(\color{red}{-p}+\color{orange}{\frac{11}{18}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{4}{5}p+\frac{11}{18}b-\frac{11}{18}.\frac{4}{5}& \text{Uitwerken } \\ & =-bp+\frac{4}{5}p+\frac{11}{18}b-\frac{44}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{4}{5}p+\frac{11}{18}b-\frac{22}{45} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{10}{4})(q+\frac{-14}{2})& =(\color{red}{a}+\color{orange}{\frac{-5}{2}}).(\color{green}{q}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-7)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = aq-7a-\frac{5}{2}q+\frac{5}{2}.7& \text{Uitwerken } \\ & =aq-7a-\frac{5}{2}q+\frac{35}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+15)(\frac{11}{5}+q)& =(\color{red}{a}+\color{orange}{15}).(\color{green}{q}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(15)} . \color{green}{(q)} + \color{orange}{(15)} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{5}a+15q+15.\frac{11}{5}& \text{Uitwerken } \\ & =aq+\frac{11}{5}a+15q+\frac{165}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{11}{5}a+15q+33 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{11}{16})(\frac{-3}{16}+q)& =(\color{red}{p}+\color{orange}{\frac{-11}{16}}).(\color{green}{q}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{16}p-\frac{11}{16}q+\frac{11}{16}.\frac{3}{16}& \text{Uitwerken } \\ & =pq-\frac{3}{16}p-\frac{11}{16}q+\frac{33}{256} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-10}{18})(\frac{-14}{20}-a)& =(\color{red}{a}+\color{orange}{\frac{-5}{9}}).(\color{green}{-a}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{7}{10}a+\frac{5}{9}a+\frac{5}{9}.\frac{7}{10}& \text{Uitwerken } \\ & =-a^2+((\frac{-7}{10})+\frac{5}{9})a+(\frac{-35}{90}) & \text{Neem samen} \\ &=-a^2-\frac{13}{90}a+(\frac{-35}{90}) & \text{Maak de som} \\ &=-a^2-\frac{13}{90}a+(\frac{-7}{18}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(q+\frac{11}{7})((-15)+q)& =(\color{red}{q}+\color{orange}{\frac{11}{7}}).(\color{green}{q}+\color{blue}{(-15)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-15)} + \color{orange}{(\frac{11}{7})} . \color{green}{(q)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = qq-15q+\frac{11}{7}q-\frac{11}{7}.15& \text{Uitwerken } \\ & =q^2+((-15)+\frac{11}{7})q-(\frac{-165}{7}) & \text{Neem samen} \\ &=q^2-\frac{94}{7}q-(\frac{-165}{7}) & \text{Maak de som} \\\end{align}\)
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