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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{20}{5})(\frac{4}{17}+b)& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{17}p-4b-4.\frac{4}{17}& \text{Uitwerken } \\ & =bp+\frac{4}{17}p-4b-\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{20}+q)(\frac{7}{3}+a)& =(\color{red}{q}+\color{orange}{\frac{-13}{20}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{3}q-\frac{13}{20}a-\frac{13}{20}.\frac{7}{3}& \text{Uitwerken } \\ & =aq+\frac{7}{3}q-\frac{13}{20}a-\frac{91}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{6}+q)(\frac{-7}{19}-b)& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{-b}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{19}q-\frac{5}{6}b-\frac{5}{6}.\frac{7}{19}& \text{Uitwerken } \\ & =-bq-\frac{7}{19}q-\frac{5}{6}b-\frac{35}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+(-8))(\frac{-19}{6}-p)& =(\color{red}{p}+\color{orange}{(-8)}).(\color{green}{-p}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(-8)} . \color{green}{(-p)} + \color{orange}{(-8)} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{6}p+8p+8.\frac{19}{6}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{6})+8)p+(\frac{-152}{6}) & \text{Neem samen} \\ &=-p^2+\frac{29}{6}p+(\frac{-152}{6}) & \text{Maak de som} \\ &=-p^2+\frac{29}{6}p+(\frac{-76}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{2}+a)(b+\frac{1}{2})& =(\color{red}{a}+\color{orange}{\frac{13}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{13}{2})} . \color{green}{(b)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a+\frac{13}{2}b+\frac{13}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a+\frac{13}{2}b+\frac{13}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{11}{15})(\frac{14}{4}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{15}}).(\color{green}{-b}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{2}p+\frac{11}{15}b-\frac{11}{15}.\frac{7}{2}& \text{Uitwerken } \\ & =-bp+\frac{7}{2}p+\frac{11}{15}b-\frac{77}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-11}{20})(p-\frac{16}{16})& =(\color{red}{x}+\color{orange}{\frac{-11}{20}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x-\frac{11}{20}p+\frac{11}{20}.1& \text{Uitwerken } \\ & =px-1x-\frac{11}{20}p+\frac{11}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-4}{10})(p+\frac{-2}{11})& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{11}b-\frac{2}{5}p+\frac{2}{5}.\frac{2}{11}& \text{Uitwerken } \\ & =bp-\frac{2}{11}b-\frac{2}{5}p+\frac{4}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-18}{19})(p+19)& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{p}+\color{blue}{19})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(19)} + \color{orange}{(\frac{-18}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = bp+19b-\frac{18}{19}p-\frac{18}{19}.19& \text{Uitwerken } \\ & =bp+19b-\frac{18}{19}p-\frac{342}{19} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+19b-\frac{18}{19}p-18 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{12}{11})(\frac{18}{16}-a)& =(\color{red}{p}+\color{orange}{\frac{-12}{11}}).(\color{green}{-a}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{8}p+\frac{12}{11}a-\frac{12}{11}.\frac{9}{8}& \text{Uitwerken } \\ & =-ap+\frac{9}{8}p+\frac{12}{11}a-\frac{108}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{9}{8}p+\frac{12}{11}a-\frac{27}{22} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{15}-x)(\frac{18}{5}+a)& =(\color{red}{-x}+\color{orange}{\frac{14}{15}}).(\color{green}{a}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{14}{15})} . \color{green}{(a)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{18}{5}x+\frac{14}{15}a+\frac{14}{15}.\frac{18}{5}& \text{Uitwerken } \\ & =-ax-\frac{18}{5}x+\frac{14}{15}a+\frac{252}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{18}{5}x+\frac{14}{15}a+\frac{84}{25} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}((-5)-b)(\frac{15}{3}-x)& =(\color{red}{-b}+\color{orange}{(-5)}).(\color{green}{-x}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(5)} + \color{orange}{(-5)} . \color{green}{(-x)} + \color{orange}{(-5)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bx-5b+5x-5.5& \text{Uitwerken } \\ & =bx-5b+5x-25 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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