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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{20}{5})(a+\frac{-3}{12})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{4}a-4a+4.\frac{1}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{4})+(-4))a+\frac{4}{4} & \text{Neem samen} \\ &=a^2-\frac{17}{4}a+\frac{4}{4} & \text{Maak de som} \\ &=a^2-\frac{17}{4}a+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-5}{6})(\frac{-2}{9}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{a}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{9}x+\frac{5}{6}a-\frac{5}{6}.\frac{2}{9}& \text{Uitwerken } \\ & =ax-\frac{2}{9}x+\frac{5}{6}a-\frac{10}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{2}{9}x+\frac{5}{6}a-\frac{5}{27} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-5}{3})(\frac{-20}{10}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ax-2x+\frac{5}{3}a-\frac{5}{3}.2& \text{Uitwerken } \\ & =ax-2x+\frac{5}{3}a-\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-(-5))(p+\frac{-12}{3})& =(\color{red}{p}+\color{orange}{5}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pp-4p+5p-5.4& \text{Uitwerken } \\ & =p^2+((-4)+5)p-(-20) & \text{Neem samen} \\ &=p^2+1p-(-20) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{9}-x)(b+\frac{19}{10})& =(\color{red}{-x}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{10}x+\frac{4}{9}b+\frac{4}{9}.\frac{19}{10}& \text{Uitwerken } \\ & =-bx-\frac{19}{10}x+\frac{4}{9}b+\frac{76}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{19}{10}x+\frac{4}{9}b+\frac{38}{45} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-6}{11})(\frac{-15}{10}+x)& =(\color{red}{p}+\color{orange}{\frac{-6}{11}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{2}p-\frac{6}{11}x+\frac{6}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =px-\frac{3}{2}p-\frac{6}{11}x+\frac{18}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{3}{2}p-\frac{6}{11}x+\frac{9}{11} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{12}{11})(q-\frac{-4}{9})& =(\color{red}{q}+\color{orange}{\frac{12}{11}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{4}{9}q+\frac{12}{11}q+\frac{12}{11}.\frac{4}{9}& \text{Uitwerken } \\ & =q^2+(\frac{4}{9}+\frac{12}{11})q+\frac{48}{99} & \text{Neem samen} \\ &=q^2+\frac{152}{99}q+\frac{48}{99} & \text{Maak de som} \\ &=q^2+\frac{152}{99}q+\frac{16}{33} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{3}{20}+x)(\frac{-18}{12}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{20}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{3}{20})} . \color{green}{(x)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{2}x+\frac{3}{20}x-\frac{3}{20}.\frac{3}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{2})+\frac{3}{20})x-(\frac{-9}{40}) & \text{Neem samen} \\ &=x^2-\frac{27}{20}x-(\frac{-9}{40}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{16}+a)(x+\frac{14}{7})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2a-\frac{1}{2}x-\frac{1}{2}.2& \text{Uitwerken } \\ & =ax+2a-\frac{1}{2}x-\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+2a-\frac{1}{2}x-1 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+(-2))(\frac{6}{19}+a)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{19}p-2a-2.\frac{6}{19}& \text{Uitwerken } \\ & =ap+\frac{6}{19}p-2a-\frac{12}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{1}{16}+p)(b-14)& =(\color{red}{p}+\color{orange}{\frac{1}{16}}).(\color{green}{b}+\color{blue}{(-14)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-14)} + \color{orange}{(\frac{1}{16})} . \color{green}{(b)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = bp-14p+\frac{1}{16}b-\frac{1}{16}.14& \text{Uitwerken } \\ & =bp-14p+\frac{1}{16}b-\frac{14}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-14p+\frac{1}{16}b-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-2}{18})(p+\frac{-15}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{9}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x-\frac{1}{9}p+\frac{1}{9}.1& \text{Uitwerken } \\ & =px-1x-\frac{1}{9}p+\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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