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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{15}-a)(\frac{10}{14}+x)& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{7}a-\frac{4}{3}x-\frac{4}{3}.\frac{5}{7}& \text{Uitwerken } \\ & =-ax-\frac{5}{7}a-\frac{4}{3}x-\frac{20}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{17}-a)(\frac{15}{18}-b)& =(\color{red}{-a}+\color{orange}{\frac{7}{17}}).(\color{green}{-b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{7}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{6}a-\frac{7}{17}b+\frac{7}{17}.\frac{5}{6}& \text{Uitwerken } \\ & =ab-\frac{5}{6}a-\frac{7}{17}b+\frac{35}{102} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{3}{16})(p+\frac{-7}{14})& =(\color{red}{x}+\color{orange}{\frac{-3}{16}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{2}x-\frac{3}{16}p+\frac{3}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =px-\frac{1}{2}x-\frac{3}{16}p+\frac{3}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-(-6))(\frac{8}{3}-a)& =(\color{red}{x}+\color{orange}{6}).(\color{green}{-a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(6)} . \color{green}{(-a)} + \color{orange}{(6)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{8}{3}x-6a+6.\frac{8}{3}& \text{Uitwerken } \\ & =-ax+\frac{8}{3}x-6a+\frac{48}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{8}{3}x-6a+16 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{16}-p)(p+\frac{-13}{6})& =(\color{red}{-p}+\color{orange}{\frac{13}{16}}).(\color{green}{p}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{13}{16})} . \color{green}{(p)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{13}{6}p+\frac{13}{16}p-\frac{13}{16}.\frac{13}{6}& \text{Uitwerken } \\ & =-p^2+(\frac{13}{6}+\frac{13}{16})p-\frac{169}{96} & \text{Neem samen} \\ &=-p^2+\frac{143}{48}p-\frac{169}{96} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{4}-x)(a+\frac{-9}{16})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{16}x-\frac{1}{2}a+\frac{1}{2}.\frac{9}{16}& \text{Uitwerken } \\ & =-ax+\frac{9}{16}x-\frac{1}{2}a+\frac{9}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{15}+b)(\frac{18}{11}-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{15}}).(\color{green}{-q}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{18}{11}b+\frac{1}{15}q-\frac{1}{15}.\frac{18}{11}& \text{Uitwerken } \\ & =-bq+\frac{18}{11}b+\frac{1}{15}q-\frac{18}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{18}{11}b+\frac{1}{15}q-\frac{6}{55} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-18}{5})(\frac{-10}{8}-x)& =(\color{red}{b}+\color{orange}{\frac{18}{5}}).(\color{green}{-x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{18}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{4}b-\frac{18}{5}x-\frac{18}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =-bx-\frac{5}{4}b-\frac{18}{5}x-\frac{90}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{4}b-\frac{18}{5}x-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-6}{2})(b-\frac{3}{18})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{6}x+3b-3.\frac{1}{6}& \text{Uitwerken } \\ & =bx-\frac{1}{6}x+3b-\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{6}x+3b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-1}{2})(b+\frac{-17}{20})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{20}q-\frac{1}{2}b+\frac{1}{2}.\frac{17}{20}& \text{Uitwerken } \\ & =bq-\frac{17}{20}q-\frac{1}{2}b+\frac{17}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-16}{11})(q-\frac{19}{9})& =(\color{red}{q}+\color{orange}{\frac{-16}{11}}).(\color{green}{q}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{9}q-\frac{16}{11}q+\frac{16}{11}.\frac{19}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{9})+(\frac{-16}{11}))q+\frac{304}{99} & \text{Neem samen} \\ &=q^2-\frac{353}{99}q+\frac{304}{99} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-4}{10})(\frac{-14}{17}+a)& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{14}{17}b-\frac{2}{5}a+\frac{2}{5}.\frac{14}{17}& \text{Uitwerken } \\ & =ab-\frac{14}{17}b-\frac{2}{5}a+\frac{28}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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