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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{6}+q)(\frac{15}{7}-x)& =(\color{red}{q}+\color{orange}{\frac{7}{6}}).(\color{green}{-x}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{15}{7}q-\frac{7}{6}x+\frac{7}{6}.\frac{15}{7}& \text{Uitwerken } \\ & =-qx+\frac{15}{7}q-\frac{7}{6}x+\frac{105}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{15}{7}q-\frac{7}{6}x+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a+\frac{16}{11})(p+14)& =(\color{red}{a}+\color{orange}{\frac{16}{11}}).(\color{green}{p}+\color{blue}{14})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(14)} + \color{orange}{(\frac{16}{11})} . \color{green}{(p)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = ap+14a+\frac{16}{11}p+\frac{16}{11}.14& \text{Uitwerken } \\ & =ap+14a+\frac{16}{11}p+\frac{224}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{11}+a)(\frac{7}{7}-a)& =(\color{red}{a}+\color{orange}{\frac{13}{11}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{13}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aa+1a-\frac{13}{11}a+\frac{13}{11}.1& \text{Uitwerken } \\ & =-a^2+(1+(\frac{-13}{11}))a+(\frac{-13}{11}) & \text{Neem samen} \\ &=-a^2-\frac{2}{11}a+(\frac{-13}{11}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{16}-p)(p+(-11))& =(\color{red}{-p}+\color{orange}{\frac{5}{4}}).(\color{green}{p}+\color{blue}{(-11)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-11)} + \color{orange}{(\frac{5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = -pp+11p+\frac{5}{4}p-\frac{5}{4}.11& \text{Uitwerken } \\ & =-p^2+(11+\frac{5}{4})p-\frac{55}{4} & \text{Neem samen} \\ &=-p^2+\frac{49}{4}p-\frac{55}{4} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-2}{12})(\frac{-9}{2}-a)& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{-a}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{2}x+\frac{1}{6}a+\frac{1}{6}.\frac{9}{2}& \text{Uitwerken } \\ & =-ax-\frac{9}{2}x+\frac{1}{6}a+\frac{9}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{9}{2}x+\frac{1}{6}a+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{13}-a)(p-\frac{2}{13})& =(\color{red}{-a}+\color{orange}{\frac{16}{13}}).(\color{green}{p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{16}{13})} . \color{green}{(p)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{13}a+\frac{16}{13}p-\frac{16}{13}.\frac{2}{13}& \text{Uitwerken } \\ & =-ap+\frac{2}{13}a+\frac{16}{13}p-\frac{32}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{12}+p)(\frac{-17}{4}+a)& =(\color{red}{p}+\color{orange}{\frac{-7}{6}}).(\color{green}{a}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{4}p-\frac{7}{6}a+\frac{7}{6}.\frac{17}{4}& \text{Uitwerken } \\ & =ap-\frac{17}{4}p-\frac{7}{6}a+\frac{119}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{2}{17})(p+\frac{-9}{8})& =(\color{red}{x}+\color{orange}{\frac{-2}{17}}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{8}x-\frac{2}{17}p+\frac{2}{17}.\frac{9}{8}& \text{Uitwerken } \\ & =px-\frac{9}{8}x-\frac{2}{17}p+\frac{18}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{8}x-\frac{2}{17}p+\frac{9}{68} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{18}{2})(\frac{15}{5}+a)& =(\color{red}{b}+\color{orange}{(-9)}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(-9)} . \color{green}{(a)} + \color{orange}{(-9)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ab+3b-9a-9.3& \text{Uitwerken } \\ & =ab+3b-9a-27 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-1}{13}-b)(\frac{-7}{19}+p)& =(\color{red}{-b}+\color{orange}{\frac{-1}{13}}).(\color{green}{p}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{19}b-\frac{1}{13}p+\frac{1}{13}.\frac{7}{19}& \text{Uitwerken } \\ & =-bp+\frac{7}{19}b-\frac{1}{13}p+\frac{7}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{3}{4})(q+\frac{-9}{5})& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{5}b-\frac{3}{4}q+\frac{3}{4}.\frac{9}{5}& \text{Uitwerken } \\ & =bq-\frac{9}{5}b-\frac{3}{4}q+\frac{27}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{9}{2})(p-\frac{-11}{19})& =(\color{red}{x}+\color{orange}{\frac{-9}{2}}).(\color{green}{p}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{19}x-\frac{9}{2}p-\frac{9}{2}.\frac{11}{19}& \text{Uitwerken } \\ & =px+\frac{11}{19}x-\frac{9}{2}p-\frac{99}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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