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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{5}{11})(\frac{18}{13}+b)& =(\color{red}{q}+\color{orange}{\frac{5}{11}}).(\color{green}{b}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{5}{11})} . \color{green}{(b)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{13}q+\frac{5}{11}b+\frac{5}{11}.\frac{18}{13}& \text{Uitwerken } \\ & =bq+\frac{18}{13}q+\frac{5}{11}b+\frac{90}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{4}{2})(p-20)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{(-20)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-20)} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = ap-20a+2p-2.20& \text{Uitwerken } \\ & =ap-20a+2p-40 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{1}{3})(\frac{12}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{-q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{3}b-\frac{1}{3}q+\frac{1}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =-bq+\frac{4}{3}b-\frac{1}{3}q+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{3}-b)(b-\frac{-8}{4})& =(\color{red}{-b}+\color{orange}{4}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(2)} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bb-2b+4b+4.2& \text{Uitwerken } \\ & =-b^2+((-2)+4)b+(-8) & \text{Neem samen} \\ &=-b^2+2b+(-8) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{8}+q)(q+\frac{-7}{20})& =(\color{red}{q}+\color{orange}{\frac{-15}{8}}).(\color{green}{q}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{20}q-\frac{15}{8}q+\frac{15}{8}.\frac{7}{20}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{20})+(\frac{-15}{8}))q+\frac{105}{160} & \text{Neem samen} \\ &=q^2-\frac{89}{40}q+\frac{105}{160} & \text{Maak de som} \\ &=q^2-\frac{89}{40}q+\frac{21}{32} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-10}{2}+p)(\frac{20}{19}-a)& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{-a}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(-5)} . \color{green}{(-a)} + \color{orange}{(-5)} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{20}{19}p+5a-5.\frac{20}{19}& \text{Uitwerken } \\ & =-ap+\frac{20}{19}p+5a-\frac{100}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-12}{16})(q-\frac{14}{5})& =(\color{red}{b}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{5}b+\frac{3}{4}q-\frac{3}{4}.\frac{14}{5}& \text{Uitwerken } \\ & =bq-\frac{14}{5}b+\frac{3}{4}q-\frac{42}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{14}{5}b+\frac{3}{4}q-\frac{21}{10} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-7}{5}+b)(\frac{-15}{5}-p)& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{-p}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-7}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bp-3b+\frac{7}{5}p+\frac{7}{5}.3& \text{Uitwerken } \\ & =-bp-3b+\frac{7}{5}p+\frac{21}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-18}{10})(a+\frac{14}{2})& =(\color{red}{b}+\color{orange}{\frac{9}{5}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(7)} + \color{orange}{(\frac{9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = ab+7b+\frac{9}{5}a+\frac{9}{5}.7& \text{Uitwerken } \\ & =ab+7b+\frac{9}{5}a+\frac{63}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{8}{12})(a-\frac{9}{20})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{20}p+\frac{2}{3}a-\frac{2}{3}.\frac{9}{20}& \text{Uitwerken } \\ & =ap-\frac{9}{20}p+\frac{2}{3}a-\frac{18}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{20}p+\frac{2}{3}a-\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{11}-x)(\frac{-2}{2}+b)& =(\color{red}{-x}+\color{orange}{\frac{-19}{11}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x-\frac{19}{11}b+\frac{19}{11}.1& \text{Uitwerken } \\ & =-bx+1x-\frac{19}{11}b+\frac{19}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{16}+x)(\frac{-20}{5}+a)& =(\color{red}{x}+\color{orange}{\frac{-15}{16}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-15}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ax-4x-\frac{15}{16}a+\frac{15}{16}.4& \text{Uitwerken } \\ & =ax-4x-\frac{15}{16}a+\frac{60}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-4x-\frac{15}{16}a+\frac{15}{4} & \text{Vereenvoudig} \\\end{align}\)
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