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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{8}-b)(b-\frac{-14}{18})& =(\color{red}{-b}+\color{orange}{\frac{15}{8}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{9}b+\frac{15}{8}b+\frac{15}{8}.\frac{7}{9}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{9})+\frac{15}{8})b+(\frac{-105}{72}) & \text{Neem samen} \\ &=-b^2+\frac{79}{72}b+(\frac{-105}{72}) & \text{Maak de som} \\ &=-b^2+\frac{79}{72}b+(\frac{-35}{24}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{2}+q)(\frac{10}{6}+q)& =(\color{red}{q}+\color{orange}{\frac{7}{2}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{3}q+\frac{7}{2}q+\frac{7}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =q^2+(\frac{5}{3}+\frac{7}{2})q+\frac{35}{6} & \text{Neem samen} \\ &=q^2+\frac{31}{6}q+\frac{35}{6} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(q-\frac{1}{9})(x+\frac{-1}{18})& =(\color{red}{q}+\color{orange}{\frac{-1}{9}}).(\color{green}{x}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{18}q-\frac{1}{9}x+\frac{1}{9}.\frac{1}{18}& \text{Uitwerken } \\ & =qx-\frac{1}{18}q-\frac{1}{9}x+\frac{1}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}((-19)-q)(a+\frac{-8}{8})& =(\color{red}{-q}+\color{orange}{(-19)}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(-19)} . \color{green}{(a)} + \color{orange}{(-19)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q-19a+19.1& \text{Uitwerken } \\ & =-aq+1q-19a+19 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{15}{17}-a)(p+\frac{-9}{8})& =(\color{red}{-a}+\color{orange}{\frac{15}{17}}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{15}{17})} . \color{green}{(p)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{8}a+\frac{15}{17}p-\frac{15}{17}.\frac{9}{8}& \text{Uitwerken } \\ & =-ap+\frac{9}{8}a+\frac{15}{17}p-\frac{135}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{8}{13})(q+\frac{13}{7})& =(\color{red}{a}+\color{orange}{\frac{8}{13}}).(\color{green}{q}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{8}{13})} . \color{green}{(q)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{7}a+\frac{8}{13}q+\frac{8}{13}.\frac{13}{7}& \text{Uitwerken } \\ & =aq+\frac{13}{7}a+\frac{8}{13}q+\frac{104}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{13}{7}a+\frac{8}{13}q+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{11}+x)(q-\frac{-6}{15})& =(\color{red}{x}+\color{orange}{\frac{-19}{11}}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{5}x-\frac{19}{11}q-\frac{19}{11}.\frac{2}{5}& \text{Uitwerken } \\ & =qx+\frac{2}{5}x-\frac{19}{11}q-\frac{38}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{11}-b)(\frac{5}{16}+b)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{16}b+1b+1.\frac{5}{16}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{16})+1)b+(\frac{-5}{16}) & \text{Neem samen} \\ &=-b^2+\frac{11}{16}b+(\frac{-5}{16}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-12}{19}-b)(\frac{-3}{17}-q)& =(\color{red}{-b}+\color{orange}{\frac{-12}{19}}).(\color{green}{-q}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{17}b+\frac{12}{19}q+\frac{12}{19}.\frac{3}{17}& \text{Uitwerken } \\ & =bq+\frac{3}{17}b+\frac{12}{19}q+\frac{36}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-3}{18}-a)(\frac{-16}{6}-p)& =(\color{red}{-a}+\color{orange}{\frac{-1}{6}}).(\color{green}{-p}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{3}a+\frac{1}{6}p+\frac{1}{6}.\frac{8}{3}& \text{Uitwerken } \\ & =ap+\frac{8}{3}a+\frac{1}{6}p+\frac{8}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{8}{3}a+\frac{1}{6}p+\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-9}{16})(\frac{17}{7}-a)& =(\color{red}{x}+\color{orange}{\frac{-9}{16}}).(\color{green}{-a}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{7}x+\frac{9}{16}a-\frac{9}{16}.\frac{17}{7}& \text{Uitwerken } \\ & =-ax+\frac{17}{7}x+\frac{9}{16}a-\frac{153}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-11}{18}+p)(\frac{15}{17}-a)& =(\color{red}{p}+\color{orange}{\frac{-11}{18}}).(\color{green}{-a}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{15}{17}p+\frac{11}{18}a-\frac{11}{18}.\frac{15}{17}& \text{Uitwerken } \\ & =-ap+\frac{15}{17}p+\frac{11}{18}a-\frac{165}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{15}{17}p+\frac{11}{18}a-\frac{55}{102} & \text{Vereenvoudig} \\\end{align}\)
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