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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-13}{16})(a-\frac{-4}{3})& =(\color{red}{p}+\color{orange}{\frac{-13}{16}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}p-\frac{13}{16}a-\frac{13}{16}.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}p-\frac{13}{16}a-\frac{52}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{3}p-\frac{13}{16}a-\frac{13}{12} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{14}-a)(\frac{-1}{10}-p)& =(\color{red}{-a}+\color{orange}{\frac{-1}{7}}).(\color{green}{-p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{10}a+\frac{1}{7}p+\frac{1}{7}.\frac{1}{10}& \text{Uitwerken } \\ & =ap+\frac{1}{10}a+\frac{1}{7}p+\frac{1}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{12}{12})(x-\frac{3}{17})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{17}a-1x+1.\frac{3}{17}& \text{Uitwerken } \\ & =ax-\frac{3}{17}a-1x+\frac{3}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-15}{9})(b+\frac{-20}{14})& =(\color{red}{a}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{10}{7}a-\frac{5}{3}b+\frac{5}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =ab-\frac{10}{7}a-\frac{5}{3}b+\frac{50}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{8}{19})(\frac{18}{9}+q)& =(\color{red}{p}+\color{orange}{\frac{8}{19}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{8}{19})} . \color{green}{(q)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p+\frac{8}{19}q+\frac{8}{19}.2& \text{Uitwerken } \\ & =pq+2p+\frac{8}{19}q+\frac{16}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{5}+p)(b+\frac{10}{9})& =(\color{red}{p}+\color{orange}{\frac{17}{5}}).(\color{green}{b}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{17}{5})} . \color{green}{(b)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{10}{9}p+\frac{17}{5}b+\frac{17}{5}.\frac{10}{9}& \text{Uitwerken } \\ & =bp+\frac{10}{9}p+\frac{17}{5}b+\frac{170}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{10}{9}p+\frac{17}{5}b+\frac{34}{9} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-19}{8})(x+\frac{14}{5})& =(\color{red}{x}+\color{orange}{\frac{19}{8}}).(\color{green}{x}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{14}{5}x+\frac{19}{8}x+\frac{19}{8}.\frac{14}{5}& \text{Uitwerken } \\ & =x^2+(\frac{14}{5}+\frac{19}{8})x+\frac{266}{40} & \text{Neem samen} \\ &=x^2+\frac{207}{40}x+\frac{266}{40} & \text{Maak de som} \\ &=x^2+\frac{207}{40}x+\frac{133}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-8}{10})(x-\frac{-13}{11})& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{11}p+\frac{4}{5}x+\frac{4}{5}.\frac{13}{11}& \text{Uitwerken } \\ & =px+\frac{13}{11}p+\frac{4}{5}x+\frac{52}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{14}+p)(a-\frac{5}{4})& =(\color{red}{p}+\color{orange}{\frac{-19}{14}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{4}p-\frac{19}{14}a+\frac{19}{14}.\frac{5}{4}& \text{Uitwerken } \\ & =ap-\frac{5}{4}p-\frac{19}{14}a+\frac{95}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-19}{15})(\frac{-20}{14}-p)& =(\color{red}{p}+\color{orange}{\frac{19}{15}}).(\color{green}{-p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{10}{7}p-\frac{19}{15}p-\frac{19}{15}.\frac{10}{7}& \text{Uitwerken } \\ & =-p^2+((\frac{-10}{7})+(\frac{-19}{15}))p-\frac{190}{105} & \text{Neem samen} \\ &=-p^2-\frac{283}{105}p-\frac{190}{105} & \text{Maak de som} \\ &=-p^2-\frac{283}{105}p-\frac{38}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{10}-q)(q-\frac{-10}{5})& =(\color{red}{-q}+\color{orange}{\frac{7}{10}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qq-2q+\frac{7}{10}q+\frac{7}{10}.2& \text{Uitwerken } \\ & =-q^2+((-2)+\frac{7}{10})q+(\frac{-14}{10}) & \text{Neem samen} \\ &=-q^2-\frac{13}{10}q+(\frac{-14}{10}) & \text{Maak de som} \\ &=-q^2-\frac{13}{10}q+(\frac{-7}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}((-17)+b)(\frac{-19}{20}+b)& =(\color{red}{b}+\color{orange}{(-17)}).(\color{green}{b}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(-17)} . \color{green}{(b)} + \color{orange}{(-17)} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{19}{20}b-17b+17.\frac{19}{20}& \text{Uitwerken } \\ & =b^2+((\frac{-19}{20})+(-17))b+\frac{323}{20} & \text{Neem samen} \\ &=b^2-\frac{359}{20}b+\frac{323}{20} & \text{Maak de som} \\\end{align}\)
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