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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-11}{12})(\frac{-14}{7}-q)& =(\color{red}{p}+\color{orange}{\frac{-11}{12}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-11}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2p+\frac{11}{12}q+\frac{11}{12}.2& \text{Uitwerken } \\ & =-pq-2p+\frac{11}{12}q+\frac{22}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-2p+\frac{11}{12}q+\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{14}+x)(x-\frac{1}{3})& =(\color{red}{x}+\color{orange}{\frac{15}{14}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{15}{14})} . \color{green}{(x)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{3}x+\frac{15}{14}x-\frac{15}{14}.\frac{1}{3}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{3})+\frac{15}{14})x-(\frac{-15}{42}) & \text{Neem samen} \\ &=x^2+\frac{31}{42}x-(\frac{-15}{42}) & \text{Maak de som} \\ &=x^2+\frac{31}{42}x+\frac{5}{14} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(q+\frac{16}{2})(x-\frac{15}{8})& =(\color{red}{q}+\color{orange}{8}).(\color{green}{x}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(8)} . \color{green}{(x)} + \color{orange}{(8)} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{15}{8}q+8x-8.\frac{15}{8}& \text{Uitwerken } \\ & =qx-\frac{15}{8}q+8x-\frac{120}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{15}{8}q+8x-15 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-14}{4}-x)(q+\frac{18}{17})& =(\color{red}{-x}+\color{orange}{\frac{-7}{2}}).(\color{green}{q}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{18}{17}x-\frac{7}{2}q-\frac{7}{2}.\frac{18}{17}& \text{Uitwerken } \\ & =-qx-\frac{18}{17}x-\frac{7}{2}q-\frac{126}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{18}{17}x-\frac{7}{2}q-\frac{63}{17} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{8}{11})((-9)+q)& =(\color{red}{q}+\color{orange}{\frac{-8}{11}}).(\color{green}{q}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-9)} + \color{orange}{(\frac{-8}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = qq-9q-\frac{8}{11}q+\frac{8}{11}.9& \text{Uitwerken } \\ & =q^2+((-9)+(\frac{-8}{11}))q+\frac{72}{11} & \text{Neem samen} \\ &=q^2-\frac{107}{11}q+\frac{72}{11} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{16}-p)(\frac{9}{2}+a)& =(\color{red}{-p}+\color{orange}{\frac{-11}{16}}).(\color{green}{a}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{2}p-\frac{11}{16}a-\frac{11}{16}.\frac{9}{2}& \text{Uitwerken } \\ & =-ap-\frac{9}{2}p-\frac{11}{16}a-\frac{99}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{9}-p)(\frac{-18}{18}+a)& =(\color{red}{-p}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1p+\frac{8}{9}a-\frac{8}{9}.1& \text{Uitwerken } \\ & =-ap+1p+\frac{8}{9}a-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{6}{2})(b-\frac{9}{6})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{2}x+3b-3.\frac{3}{2}& \text{Uitwerken } \\ & =bx-\frac{3}{2}x+3b-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{13}{16})(a-\frac{12}{6})& =(\color{red}{a}+\color{orange}{\frac{-13}{16}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aa-2a-\frac{13}{16}a+\frac{13}{16}.2& \text{Uitwerken } \\ & =a^2+((-2)+(\frac{-13}{16}))a+\frac{26}{16} & \text{Neem samen} \\ &=a^2-\frac{45}{16}a+\frac{26}{16} & \text{Maak de som} \\ &=a^2-\frac{45}{16}a+\frac{13}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{16}+q)(p-\frac{-5}{5})& =(\color{red}{q}+\color{orange}{\frac{9}{8}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{9}{8})} . \color{green}{(p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1q+\frac{9}{8}p+\frac{9}{8}.1& \text{Uitwerken } \\ & =pq+1q+\frac{9}{8}p+\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-13}{19})(\frac{6}{11}+a)& =(\color{red}{q}+\color{orange}{\frac{13}{19}}).(\color{green}{a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{13}{19})} . \color{green}{(a)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{11}q+\frac{13}{19}a+\frac{13}{19}.\frac{6}{11}& \text{Uitwerken } \\ & =aq+\frac{6}{11}q+\frac{13}{19}a+\frac{78}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-12}{12})(\frac{18}{3}-a)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -aq+6q+1a-1.6& \text{Uitwerken } \\ & =-aq+6q+1a-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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