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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-8}{7})(\frac{-4}{17}+p)& =(\color{red}{q}+\color{orange}{\frac{8}{7}}).(\color{green}{p}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{17}q+\frac{8}{7}p-\frac{8}{7}.\frac{4}{17}& \text{Uitwerken } \\ & =pq-\frac{4}{17}q+\frac{8}{7}p-\frac{32}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{17}{12})(x+\frac{19}{6})& =(\color{red}{b}+\color{orange}{\frac{-17}{12}}).(\color{green}{x}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{6}b-\frac{17}{12}x-\frac{17}{12}.\frac{19}{6}& \text{Uitwerken } \\ & =bx+\frac{19}{6}b-\frac{17}{12}x-\frac{323}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-2}{3})(b-\frac{9}{7})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{7}p+\frac{2}{3}b-\frac{2}{3}.\frac{9}{7}& \text{Uitwerken } \\ & =bp-\frac{9}{7}p+\frac{2}{3}b-\frac{18}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{7}p+\frac{2}{3}b-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{18}+q)(\frac{-1}{15}+a)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{15}q-1a+1.\frac{1}{15}& \text{Uitwerken } \\ & =aq-\frac{1}{15}q-1a+\frac{1}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+(-6))(\frac{10}{20}-q)& =(\color{red}{p}+\color{orange}{(-6)}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-6)} . \color{green}{(-q)} + \color{orange}{(-6)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{2}p+6q-6.\frac{1}{2}& \text{Uitwerken } \\ & =-pq+\frac{1}{2}p+6q-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{1}{2}p+6q-3 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-7}{16})(b+\frac{-18}{3})& =(\color{red}{x}+\color{orange}{\frac{7}{16}}).(\color{green}{b}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-6)} + \color{orange}{(\frac{7}{16})} . \color{green}{(b)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = bx-6x+\frac{7}{16}b-\frac{7}{16}.6& \text{Uitwerken } \\ & =bx-6x+\frac{7}{16}b-\frac{42}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-6x+\frac{7}{16}b-\frac{21}{8} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{5}-x)(b-\frac{8}{14})& =(\color{red}{-x}+\color{orange}{\frac{-17}{5}}).(\color{green}{b}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{7}x-\frac{17}{5}b+\frac{17}{5}.\frac{4}{7}& \text{Uitwerken } \\ & =-bx+\frac{4}{7}x-\frac{17}{5}b+\frac{68}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{11}-a)(x+\frac{-10}{16})& =(\color{red}{-a}+\color{orange}{\frac{4}{11}}).(\color{green}{x}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{8}a+\frac{4}{11}x-\frac{4}{11}.\frac{5}{8}& \text{Uitwerken } \\ & =-ax+\frac{5}{8}a+\frac{4}{11}x-\frac{20}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{8}a+\frac{4}{11}x-\frac{5}{22} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{20}+p)(a-\frac{20}{12})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{3}p+1a-1.\frac{5}{3}& \text{Uitwerken } \\ & =ap-\frac{5}{3}p+1a-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-14}{19})(\frac{7}{4}-q)& =(\color{red}{q}+\color{orange}{\frac{-14}{19}}).(\color{green}{-q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{7}{4}q+\frac{14}{19}q-\frac{14}{19}.\frac{7}{4}& \text{Uitwerken } \\ & =-q^2+(\frac{7}{4}+\frac{14}{19})q-\frac{98}{76} & \text{Neem samen} \\ &=-q^2+\frac{189}{76}q-\frac{98}{76} & \text{Maak de som} \\ &=-q^2+\frac{189}{76}q-\frac{49}{38} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{10}-b)(\frac{15}{11}-a)& =(\color{red}{-b}+\color{orange}{\frac{7}{10}}).(\color{green}{-a}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{7}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{11}b-\frac{7}{10}a+\frac{7}{10}.\frac{15}{11}& \text{Uitwerken } \\ & =ab-\frac{15}{11}b-\frac{7}{10}a+\frac{105}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{11}b-\frac{7}{10}a+\frac{21}{22} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+15)(\frac{11}{11}+x)& =(\color{red}{q}+\color{orange}{15}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(15)} . \color{green}{(x)} + \color{orange}{(15)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1q+15x+15.1& \text{Uitwerken } \\ & =qx+1q+15x+15 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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