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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-18}{11})(\frac{8}{15}-x)& =(\color{red}{p}+\color{orange}{\frac{18}{11}}).(\color{green}{-x}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{18}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{8}{15}p-\frac{18}{11}x+\frac{18}{11}.\frac{8}{15}& \text{Uitwerken } \\ & =-px+\frac{8}{15}p-\frac{18}{11}x+\frac{144}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{8}{15}p-\frac{18}{11}x+\frac{48}{55} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{20}-x)(p+14)& =(\color{red}{-x}+\color{orange}{\frac{-17}{20}}).(\color{green}{p}+\color{blue}{14})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(14)} + \color{orange}{(\frac{-17}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = -px-14x-\frac{17}{20}p-\frac{17}{20}.14& \text{Uitwerken } \\ & =-px-14x-\frac{17}{20}p-\frac{238}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-14x-\frac{17}{20}p-\frac{119}{10} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{8}-b)(\frac{-13}{8}-a)& =(\color{red}{-b}+\color{orange}{\frac{1}{8}}).(\color{green}{-a}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{8}b-\frac{1}{8}a-\frac{1}{8}.\frac{13}{8}& \text{Uitwerken } \\ & =ab+\frac{13}{8}b-\frac{1}{8}a-\frac{13}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-10}{19})(\frac{-8}{13}+a)& =(\color{red}{p}+\color{orange}{\frac{10}{19}}).(\color{green}{a}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{10}{19})} . \color{green}{(a)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{13}p+\frac{10}{19}a-\frac{10}{19}.\frac{8}{13}& \text{Uitwerken } \\ & =ap-\frac{8}{13}p+\frac{10}{19}a-\frac{80}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{4}{18})(\frac{17}{19}+p)& =(\color{red}{x}+\color{orange}{\frac{2}{9}}).(\color{green}{p}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{19}x+\frac{2}{9}p+\frac{2}{9}.\frac{17}{19}& \text{Uitwerken } \\ & =px+\frac{17}{19}x+\frac{2}{9}p+\frac{34}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-11}{9})(a+\frac{-15}{4})& =(\color{red}{b}+\color{orange}{\frac{-11}{9}}).(\color{green}{a}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{4}b-\frac{11}{9}a+\frac{11}{9}.\frac{15}{4}& \text{Uitwerken } \\ & =ab-\frac{15}{4}b-\frac{11}{9}a+\frac{165}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{4}b-\frac{11}{9}a+\frac{55}{12} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{4}{6}-q)(b+\frac{18}{9})& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bq-2q+\frac{2}{3}b+\frac{2}{3}.2& \text{Uitwerken } \\ & =-bq-2q+\frac{2}{3}b+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{3}{7}+a)(\frac{5}{20}-a)& =(\color{red}{a}+\color{orange}{\frac{3}{7}}).(\color{green}{-a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{3}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{4}a-\frac{3}{7}a+\frac{3}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{4}+(\frac{-3}{7}))a+(\frac{-3}{28}) & \text{Neem samen} \\ &=-a^2-\frac{5}{28}a+(\frac{-3}{28}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}((-8)-q)((-1)+a)& =(\color{red}{-q}+\color{orange}{(-8)}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(-8)} . \color{green}{(a)} + \color{orange}{(-8)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q-8a+8.1& \text{Uitwerken } \\ & =-aq+1q-8a+8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{8}+b)(\frac{-7}{17}-b)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-b}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{17}b+\frac{3}{2}b+\frac{3}{2}.\frac{7}{17}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{17})+\frac{3}{2})b+(\frac{-21}{34}) & \text{Neem samen} \\ &=-b^2+\frac{37}{34}b+(\frac{-21}{34}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-20}{16})(p-\frac{17}{11})& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{p}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{11}p+\frac{5}{4}p-\frac{5}{4}.\frac{17}{11}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{11})+\frac{5}{4})p-(\frac{-85}{44}) & \text{Neem samen} \\ &=p^2-\frac{13}{44}p-(\frac{-85}{44}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{19}+a)(a-(-2))& =(\color{red}{a}+\color{orange}{\frac{1}{19}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{1}{19})} . \color{green}{(a)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aa+2a+\frac{1}{19}a+\frac{1}{19}.2& \text{Uitwerken } \\ & =a^2+(2+\frac{1}{19})a+\frac{2}{19} & \text{Neem samen} \\ &=a^2+\frac{39}{19}a+\frac{2}{19} & \text{Maak de som} \\\end{align}\)
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