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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-19}{9})(a-\frac{15}{4})& =(\color{red}{b}+\color{orange}{\frac{-19}{9}}).(\color{green}{a}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{4}b-\frac{19}{9}a+\frac{19}{9}.\frac{15}{4}& \text{Uitwerken } \\ & =ab-\frac{15}{4}b-\frac{19}{9}a+\frac{285}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{4}b-\frac{19}{9}a+\frac{95}{12} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{11}+a)(\frac{8}{15}+a)& =(\color{red}{a}+\color{orange}{\frac{-3}{11}}).(\color{green}{a}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{8}{15}a-\frac{3}{11}a-\frac{3}{11}.\frac{8}{15}& \text{Uitwerken } \\ & =a^2+(\frac{8}{15}+(\frac{-3}{11}))a-(\frac{-24}{165}) & \text{Neem samen} \\ &=a^2+\frac{43}{165}a-(\frac{-24}{165}) & \text{Maak de som} \\ &=a^2+\frac{43}{165}a+\frac{8}{55} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{18}-b)(\frac{-1}{16}+q)& =(\color{red}{-b}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{16}b+\frac{5}{6}q-\frac{5}{6}.\frac{1}{16}& \text{Uitwerken } \\ & =-bq+\frac{1}{16}b+\frac{5}{6}q-\frac{5}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{6}{17})(\frac{8}{11}-p)& =(\color{red}{b}+\color{orange}{\frac{-6}{17}}).(\color{green}{-p}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{11}b+\frac{6}{17}p-\frac{6}{17}.\frac{8}{11}& \text{Uitwerken } \\ & =-bp+\frac{8}{11}b+\frac{6}{17}p-\frac{48}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{8}{4})(b+\frac{-9}{2})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{2}x-2b+2.\frac{9}{2}& \text{Uitwerken } \\ & =bx-\frac{9}{2}x-2b+\frac{18}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{9}{2}x-2b+9 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{9}+p)(\frac{-10}{12}+b)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{6}p+2b-2.\frac{5}{6}& \text{Uitwerken } \\ & =bp-\frac{5}{6}p+2b-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{6}p+2b-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-4}{4}-p)(b-\frac{13}{15})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{15}p-1b+1.\frac{13}{15}& \text{Uitwerken } \\ & =-bp+\frac{13}{15}p-1b+\frac{13}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{17}-q)(\frac{20}{20}-x)& =(\color{red}{-q}+\color{orange}{\frac{-12}{17}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{-12}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q+\frac{12}{17}x-\frac{12}{17}.1& \text{Uitwerken } \\ & =qx-1q+\frac{12}{17}x-\frac{12}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-15)+p)(b-\frac{8}{17})& =(\color{red}{p}+\color{orange}{(-15)}).(\color{green}{b}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(-15)} . \color{green}{(b)} + \color{orange}{(-15)} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{17}p-15b+15.\frac{8}{17}& \text{Uitwerken } \\ & =bp-\frac{8}{17}p-15b+\frac{120}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{3}-a)(\frac{-17}{4}+a)& =(\color{red}{-a}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{17}{4}a-\frac{7}{3}a+\frac{7}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =-a^2+(\frac{17}{4}+(\frac{-7}{3}))a+(\frac{-119}{12}) & \text{Neem samen} \\ &=-a^2+\frac{23}{12}a+(\frac{-119}{12}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-10}{16})(\frac{14}{12}+q)& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{q}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{5}{8})} . \color{green}{(q)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{6}a+\frac{5}{8}q+\frac{5}{8}.\frac{7}{6}& \text{Uitwerken } \\ & =aq+\frac{7}{6}a+\frac{5}{8}q+\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{17}+p)(a+\frac{-9}{19})& =(\color{red}{p}+\color{orange}{\frac{-2}{17}}).(\color{green}{a}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{19}p-\frac{2}{17}a+\frac{2}{17}.\frac{9}{19}& \text{Uitwerken } \\ & =ap-\frac{9}{19}p-\frac{2}{17}a+\frac{18}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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