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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}((-12)-b)(a-(-20))& =(\color{red}{-b}+\color{orange}{(-12)}).(\color{green}{a}+\color{blue}{20})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(20)} + \color{orange}{(-12)} . \color{green}{(a)} + \color{orange}{(-12)} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -ab-20b-12a-12.20& \text{Uitwerken } \\ & =-ab-20b-12a-240 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{17}+b)(x-\frac{-3}{4})& =(\color{red}{b}+\color{orange}{\frac{19}{17}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{19}{17})} . \color{green}{(x)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{4}b+\frac{19}{17}x+\frac{19}{17}.\frac{3}{4}& \text{Uitwerken } \\ & =bx+\frac{3}{4}b+\frac{19}{17}x+\frac{57}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-2)(p-\frac{-13}{20})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{13}{20}q-2p-2.\frac{13}{20}& \text{Uitwerken } \\ & =pq+\frac{13}{20}q-2p-\frac{26}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{13}{20}q-2p-\frac{13}{10} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{12}{17})(p-\frac{10}{9})& =(\color{red}{b}+\color{orange}{\frac{-12}{17}}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{10}{9}b-\frac{12}{17}p+\frac{12}{17}.\frac{10}{9}& \text{Uitwerken } \\ & =bp-\frac{10}{9}b-\frac{12}{17}p+\frac{120}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{10}{9}b-\frac{12}{17}p+\frac{40}{51} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{10}{20})(x+\frac{6}{8})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{4}a+\frac{1}{2}x+\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =ax+\frac{3}{4}a+\frac{1}{2}x+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-2}{9})(\frac{-18}{3}-p)& =(\color{red}{a}+\color{orange}{\frac{-2}{9}}).(\color{green}{-p}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-6)} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -ap-6a+\frac{2}{9}p+\frac{2}{9}.6& \text{Uitwerken } \\ & =-ap-6a+\frac{2}{9}p+\frac{12}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-6a+\frac{2}{9}p+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{17}{5})(\frac{11}{15}-a)& =(\color{red}{p}+\color{orange}{\frac{-17}{5}}).(\color{green}{-a}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{15}p+\frac{17}{5}a-\frac{17}{5}.\frac{11}{15}& \text{Uitwerken } \\ & =-ap+\frac{11}{15}p+\frac{17}{5}a-\frac{187}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{13}{4})(p+\frac{11}{6})& =(\color{red}{b}+\color{orange}{\frac{-13}{4}}).(\color{green}{p}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{6}b-\frac{13}{4}p-\frac{13}{4}.\frac{11}{6}& \text{Uitwerken } \\ & =bp+\frac{11}{6}b-\frac{13}{4}p-\frac{143}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{12}{10})(\frac{-17}{14}+a)& =(\color{red}{x}+\color{orange}{\frac{6}{5}}).(\color{green}{a}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{14}x+\frac{6}{5}a-\frac{6}{5}.\frac{17}{14}& \text{Uitwerken } \\ & =ax-\frac{17}{14}x+\frac{6}{5}a-\frac{102}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{14}x+\frac{6}{5}a-\frac{51}{35} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{12}+q)(\frac{-10}{5}-p)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2q+\frac{3}{4}p+\frac{3}{4}.2& \text{Uitwerken } \\ & =-pq-2q+\frac{3}{4}p+\frac{6}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-2q+\frac{3}{4}p+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{5}+p)(\frac{10}{8}-x)& =(\color{red}{p}+\color{orange}{\frac{16}{5}}).(\color{green}{-x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{16}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{4}p-\frac{16}{5}x+\frac{16}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =-px+\frac{5}{4}p-\frac{16}{5}x+\frac{80}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{5}{4}p-\frac{16}{5}x+4 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-6}{9})(a+\frac{20}{9})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{9}p+\frac{2}{3}a+\frac{2}{3}.\frac{20}{9}& \text{Uitwerken } \\ & =ap+\frac{20}{9}p+\frac{2}{3}a+\frac{40}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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