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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-13}{8})(\frac{10}{2}+q)& =(\color{red}{q}+\color{orange}{\frac{13}{8}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qq+5q+\frac{13}{8}q+\frac{13}{8}.5& \text{Uitwerken } \\ & =q^2+(5+\frac{13}{8})q+\frac{65}{8} & \text{Neem samen} \\ &=q^2+\frac{53}{8}q+\frac{65}{8} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-9}{3})(\frac{-5}{8}+p)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{8}q+3p-3.\frac{5}{8}& \text{Uitwerken } \\ & =pq-\frac{5}{8}q+3p-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{9}-q)(\frac{12}{6}-a)& =(\color{red}{-q}+\color{orange}{\frac{-20}{9}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-20}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq-2q+\frac{20}{9}a-\frac{20}{9}.2& \text{Uitwerken } \\ & =aq-2q+\frac{20}{9}a-\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{3}{7})(q-\frac{-1}{19})& =(\color{red}{a}+\color{orange}{\frac{-3}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{19}a-\frac{3}{7}q-\frac{3}{7}.\frac{1}{19}& \text{Uitwerken } \\ & =aq+\frac{1}{19}a-\frac{3}{7}q-\frac{3}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-19}{14}+q)(\frac{-13}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{-19}{14}}).(\color{green}{-q}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{13}{9}q+\frac{19}{14}q+\frac{19}{14}.\frac{13}{9}& \text{Uitwerken } \\ & =-q^2+((\frac{-13}{9})+\frac{19}{14})q+(\frac{-247}{126}) & \text{Neem samen} \\ &=-q^2-\frac{11}{126}q+(\frac{-247}{126}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-4}{8})(\frac{-2}{17}-b)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{17}q+\frac{1}{2}b+\frac{1}{2}.\frac{2}{17}& \text{Uitwerken } \\ & =-bq-\frac{2}{17}q+\frac{1}{2}b+\frac{2}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{2}{17}q+\frac{1}{2}b+\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{9}+p)(\frac{-19}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{b}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{12}p+\frac{5}{3}b-\frac{5}{3}.\frac{19}{12}& \text{Uitwerken } \\ & =bp-\frac{19}{12}p+\frac{5}{3}b-\frac{95}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{16}{17})(\frac{-15}{7}-b)& =(\color{red}{b}+\color{orange}{\frac{-16}{17}}).(\color{green}{-b}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{15}{7}b+\frac{16}{17}b+\frac{16}{17}.\frac{15}{7}& \text{Uitwerken } \\ & =-b^2+((\frac{-15}{7})+\frac{16}{17})b+(\frac{-240}{119}) & \text{Neem samen} \\ &=-b^2-\frac{143}{119}b+(\frac{-240}{119}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b-\frac{4}{4})(a+\frac{-14}{8})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{4}b-1a+1.\frac{7}{4}& \text{Uitwerken } \\ & =ab-\frac{7}{4}b-1a+\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{20}-x)(\frac{10}{12}-b)& =(\color{red}{-x}+\color{orange}{\frac{19}{20}}).(\color{green}{-b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{19}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{6}x-\frac{19}{20}b+\frac{19}{20}.\frac{5}{6}& \text{Uitwerken } \\ & =bx-\frac{5}{6}x-\frac{19}{20}b+\frac{95}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{5}{6}x-\frac{19}{20}b+\frac{19}{24} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{8}{15})(\frac{3}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{-8}{15}}).(\color{green}{x}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{19}b-\frac{8}{15}x-\frac{8}{15}.\frac{3}{19}& \text{Uitwerken } \\ & =bx+\frac{3}{19}b-\frac{8}{15}x-\frac{24}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{19}b-\frac{8}{15}x-\frac{8}{95} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{19}+q)(\frac{-19}{14}+p)& =(\color{red}{q}+\color{orange}{\frac{-9}{19}}).(\color{green}{p}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{14}q-\frac{9}{19}p+\frac{9}{19}.\frac{19}{14}& \text{Uitwerken } \\ & =pq-\frac{19}{14}q-\frac{9}{19}p+\frac{171}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{19}{14}q-\frac{9}{19}p+\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
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