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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-9}{19}+p)(b+\frac{6}{20})& =(\color{red}{p}+\color{orange}{\frac{-9}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{10}p-\frac{9}{19}b-\frac{9}{19}.\frac{3}{10}& \text{Uitwerken } \\ & =bp+\frac{3}{10}p-\frac{9}{19}b-\frac{27}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{8}-x)(\frac{12}{4}+p)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -px-3x+1p+1.3& \text{Uitwerken } \\ & =-px-3x+1p+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{3}+a)(p-\frac{14}{10})& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{5}a-\frac{10}{3}p+\frac{10}{3}.\frac{7}{5}& \text{Uitwerken } \\ & =ap-\frac{7}{5}a-\frac{10}{3}p+\frac{70}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{7}{5}a-\frac{10}{3}p+\frac{14}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{3}{18}+a)(\frac{-16}{9}+x)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{9}a+\frac{1}{6}x-\frac{1}{6}.\frac{16}{9}& \text{Uitwerken } \\ & =ax-\frac{16}{9}a+\frac{1}{6}x-\frac{16}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{16}{9}a+\frac{1}{6}x-\frac{8}{27} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-20}{7}-b)(\frac{12}{4}+b)& =(\color{red}{-b}+\color{orange}{\frac{-20}{7}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(3)} + \color{orange}{(\frac{-20}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bb-3b-\frac{20}{7}b-\frac{20}{7}.3& \text{Uitwerken } \\ & =-b^2+((-3)+(\frac{-20}{7}))b-\frac{60}{7} & \text{Neem samen} \\ &=-b^2-\frac{41}{7}b-\frac{60}{7} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b-\frac{17}{8})(a-\frac{-12}{8})& =(\color{red}{b}+\color{orange}{\frac{-17}{8}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{2}b-\frac{17}{8}a-\frac{17}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =ab+\frac{3}{2}b-\frac{17}{8}a-\frac{51}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{8}+x)(\frac{2}{15}-p)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{-p}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{15}x-\frac{3}{4}p+\frac{3}{4}.\frac{2}{15}& \text{Uitwerken } \\ & =-px+\frac{2}{15}x-\frac{3}{4}p+\frac{6}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{2}{15}x-\frac{3}{4}p+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{7}-x)(p-\frac{-12}{16})& =(\color{red}{-x}+\color{orange}{\frac{4}{7}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{4}x+\frac{4}{7}p+\frac{4}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =-px-\frac{3}{4}x+\frac{4}{7}p+\frac{12}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{3}{4}x+\frac{4}{7}p+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-3}{13})(a+\frac{6}{14})& =(\color{red}{q}+\color{orange}{\frac{-3}{13}}).(\color{green}{a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{7}q-\frac{3}{13}a-\frac{3}{13}.\frac{3}{7}& \text{Uitwerken } \\ & =aq+\frac{3}{7}q-\frac{3}{13}a-\frac{9}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{10}{18})(p-\frac{12}{4})& =(\color{red}{p}+\color{orange}{\frac{5}{9}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{5}{9})} . \color{green}{(p)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pp-3p+\frac{5}{9}p-\frac{5}{9}.3& \text{Uitwerken } \\ & =p^2+((-3)+\frac{5}{9})p-(\frac{-15}{9}) & \text{Neem samen} \\ &=p^2-\frac{22}{9}p-(\frac{-15}{9}) & \text{Maak de som} \\ &=p^2-\frac{22}{9}p+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(q+\frac{20}{3})(\frac{12}{15}+x)& =(\color{red}{q}+\color{orange}{\frac{20}{3}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{20}{3})} . \color{green}{(x)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{5}q+\frac{20}{3}x+\frac{20}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =qx+\frac{4}{5}q+\frac{20}{3}x+\frac{80}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{5}q+\frac{20}{3}x+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-12}{7})(\frac{18}{9}+q)& =(\color{red}{a}+\color{orange}{\frac{-12}{7}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-12}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a-\frac{12}{7}q-\frac{12}{7}.2& \text{Uitwerken } \\ & =aq+2a-\frac{12}{7}q-\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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