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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-11}{15}-p)(\frac{-9}{7}-b)& =(\color{red}{-p}+\color{orange}{\frac{-11}{15}}).(\color{green}{-b}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{7}p+\frac{11}{15}b+\frac{11}{15}.\frac{9}{7}& \text{Uitwerken } \\ & =bp+\frac{9}{7}p+\frac{11}{15}b+\frac{99}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{7}p+\frac{11}{15}b+\frac{33}{35} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-8}{9})(b+\frac{15}{6})& =(\color{red}{q}+\color{orange}{\frac{8}{9}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{2}q+\frac{8}{9}b+\frac{8}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =bq+\frac{5}{2}q+\frac{8}{9}b+\frac{40}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{2}q+\frac{8}{9}b+\frac{20}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{12}-a)(\frac{4}{20}+b)& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{5}a-\frac{3}{4}b-\frac{3}{4}.\frac{1}{5}& \text{Uitwerken } \\ & =-ab-\frac{1}{5}a-\frac{3}{4}b-\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}((-3)+p)(\frac{-9}{18}+b)& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}p-3b+3.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}p-3b+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-17}{7})(\frac{8}{5}-a)& =(\color{red}{b}+\color{orange}{\frac{-17}{7}}).(\color{green}{-a}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{5}b+\frac{17}{7}a-\frac{17}{7}.\frac{8}{5}& \text{Uitwerken } \\ & =-ab+\frac{8}{5}b+\frac{17}{7}a-\frac{136}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{13}{12})(b-\frac{4}{8})& =(\color{red}{a}+\color{orange}{\frac{-13}{12}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}a-\frac{13}{12}b+\frac{13}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}a-\frac{13}{12}b+\frac{13}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{4}-a)(x+\frac{-1}{11})& =(\color{red}{-a}+\color{orange}{\frac{19}{4}}).(\color{green}{x}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{19}{4})} . \color{green}{(x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{11}a+\frac{19}{4}x-\frac{19}{4}.\frac{1}{11}& \text{Uitwerken } \\ & =-ax+\frac{1}{11}a+\frac{19}{4}x-\frac{19}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-7}{20})(b+\frac{9}{19})& =(\color{red}{p}+\color{orange}{\frac{7}{20}}).(\color{green}{b}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{7}{20})} . \color{green}{(b)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{19}p+\frac{7}{20}b+\frac{7}{20}.\frac{9}{19}& \text{Uitwerken } \\ & =bp+\frac{9}{19}p+\frac{7}{20}b+\frac{63}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{12}{3}+a)(\frac{-18}{3}-q)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-6)} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -aq-6a-4q-4.6& \text{Uitwerken } \\ & =-aq-6a-4q-24 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-10}{8})(b+\frac{-2}{5})& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{5}a+\frac{5}{4}b-\frac{5}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =ab-\frac{2}{5}a+\frac{5}{4}b-\frac{10}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{5}a+\frac{5}{4}b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{13}{18})(q+\frac{3}{13})& =(\color{red}{b}+\color{orange}{\frac{-13}{18}}).(\color{green}{q}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{13}b-\frac{13}{18}q-\frac{13}{18}.\frac{3}{13}& \text{Uitwerken } \\ & =bq+\frac{3}{13}b-\frac{13}{18}q-\frac{39}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{13}b-\frac{13}{18}q-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{11}-p)(\frac{1}{18}+b)& =(\color{red}{-p}+\color{orange}{\frac{8}{11}}).(\color{green}{b}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{8}{11})} . \color{green}{(b)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{18}p+\frac{8}{11}b+\frac{8}{11}.\frac{1}{18}& \text{Uitwerken } \\ & =-bp-\frac{1}{18}p+\frac{8}{11}b+\frac{8}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{1}{18}p+\frac{8}{11}b+\frac{4}{99} & \text{Vereenvoudig} \\\end{align}\)
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