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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-9}{7}+x)((-19)+x)& =(\color{red}{x}+\color{orange}{\frac{-9}{7}}).(\color{green}{x}+\color{blue}{(-19)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-19)} + \color{orange}{(\frac{-9}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = xx-19x-\frac{9}{7}x+\frac{9}{7}.19& \text{Uitwerken } \\ & =x^2+((-19)+(\frac{-9}{7}))x+\frac{171}{7} & \text{Neem samen} \\ &=x^2-\frac{142}{7}x+\frac{171}{7} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q+\frac{6}{12})(a-\frac{-11}{11})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1q+\frac{1}{2}a+\frac{1}{2}.1& \text{Uitwerken } \\ & =aq+1q+\frac{1}{2}a+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{7}{13}+x)(\frac{4}{7}-a)& =(\color{red}{x}+\color{orange}{\frac{7}{13}}).(\color{green}{-a}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{7}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{7}x-\frac{7}{13}a+\frac{7}{13}.\frac{4}{7}& \text{Uitwerken } \\ & =-ax+\frac{4}{7}x-\frac{7}{13}a+\frac{28}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{4}{7}x-\frac{7}{13}a+\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{10}{7})(a+\frac{19}{8})& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{a}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{8}x+\frac{10}{7}a+\frac{10}{7}.\frac{19}{8}& \text{Uitwerken } \\ & =ax+\frac{19}{8}x+\frac{10}{7}a+\frac{190}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{19}{8}x+\frac{10}{7}a+\frac{95}{28} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-19}{18}+a)(p-\frac{-11}{19})& =(\color{red}{a}+\color{orange}{\frac{-19}{18}}).(\color{green}{p}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{19}a-\frac{19}{18}p-\frac{19}{18}.\frac{11}{19}& \text{Uitwerken } \\ & =ap+\frac{11}{19}a-\frac{19}{18}p-\frac{209}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{11}{19}a-\frac{19}{18}p-\frac{11}{18} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-1}{3})(q+\frac{-15}{9})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{3}x+\frac{1}{3}q-\frac{1}{3}.\frac{5}{3}& \text{Uitwerken } \\ & =qx-\frac{5}{3}x+\frac{1}{3}q-\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{2}{17})(a-\frac{-7}{11})& =(\color{red}{q}+\color{orange}{\frac{2}{17}}).(\color{green}{a}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{11}q+\frac{2}{17}a+\frac{2}{17}.\frac{7}{11}& \text{Uitwerken } \\ & =aq+\frac{7}{11}q+\frac{2}{17}a+\frac{14}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{17}+p)(\frac{19}{6}-a)& =(\color{red}{p}+\color{orange}{\frac{4}{17}}).(\color{green}{-a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{4}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{6}p-\frac{4}{17}a+\frac{4}{17}.\frac{19}{6}& \text{Uitwerken } \\ & =-ap+\frac{19}{6}p-\frac{4}{17}a+\frac{76}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{19}{6}p-\frac{4}{17}a+\frac{38}{51} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{12}+b)(x-\frac{-1}{9})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{9}b+\frac{2}{3}x+\frac{2}{3}.\frac{1}{9}& \text{Uitwerken } \\ & =bx+\frac{1}{9}b+\frac{2}{3}x+\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-2}{18})(x+\frac{-12}{4})& =(\color{red}{b}+\color{orange}{\frac{-1}{9}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx-3b-\frac{1}{9}x+\frac{1}{9}.3& \text{Uitwerken } \\ & =bx-3b-\frac{1}{9}x+\frac{3}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-3b-\frac{1}{9}x+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-11}{18})(a+\frac{-8}{2})& =(\color{red}{a}+\color{orange}{\frac{11}{18}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{11}{18})} . \color{green}{(a)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aa-4a+\frac{11}{18}a-\frac{11}{18}.4& \text{Uitwerken } \\ & =a^2+((-4)+\frac{11}{18})a-(\frac{-44}{18}) & \text{Neem samen} \\ &=a^2-\frac{61}{18}a-(\frac{-44}{18}) & \text{Maak de som} \\ &=a^2-\frac{61}{18}a+\frac{22}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{3}{16}+a)(\frac{-18}{17}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{16}}).(\color{green}{-x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{3}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{18}{17}a-\frac{3}{16}x-\frac{3}{16}.\frac{18}{17}& \text{Uitwerken } \\ & =-ax-\frac{18}{17}a-\frac{3}{16}x-\frac{54}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{18}{17}a-\frac{3}{16}x-\frac{27}{136} & \text{Vereenvoudig} \\\end{align}\)
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