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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{16}+x)(17-a)& =(\color{red}{x}+\color{orange}{\frac{-15}{16}}).(\color{green}{-a}+\color{blue}{17})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(17)} + \color{orange}{(\frac{-15}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = -ax+17x+\frac{15}{16}a-\frac{15}{16}.17& \text{Uitwerken } \\ & =-ax+17x+\frac{15}{16}a-\frac{255}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{12}{14})(x-\frac{-5}{17})& =(\color{red}{b}+\color{orange}{\frac{-6}{7}}).(\color{green}{x}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{17}b-\frac{6}{7}x-\frac{6}{7}.\frac{5}{17}& \text{Uitwerken } \\ & =bx+\frac{5}{17}b-\frac{6}{7}x-\frac{30}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{10}{16}+q)(\frac{-18}{3}+p)& =(\color{red}{q}+\color{orange}{\frac{5}{8}}).(\color{green}{p}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-6)} + \color{orange}{(\frac{5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = pq-6q+\frac{5}{8}p-\frac{5}{8}.6& \text{Uitwerken } \\ & =pq-6q+\frac{5}{8}p-\frac{30}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-6q+\frac{5}{8}p-\frac{15}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{8}{8}-a)(\frac{-11}{16}+p)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{16}a+1p-1.\frac{11}{16}& \text{Uitwerken } \\ & =-ap+\frac{11}{16}a+1p-\frac{11}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{17}-b)(p-\frac{-19}{17})& =(\color{red}{-b}+\color{orange}{\frac{-8}{17}}).(\color{green}{p}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{17}b-\frac{8}{17}p-\frac{8}{17}.\frac{19}{17}& \text{Uitwerken } \\ & =-bp-\frac{19}{17}b-\frac{8}{17}p-\frac{152}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{4}{13})(q-\frac{11}{9})& =(\color{red}{q}+\color{orange}{\frac{-4}{13}}).(\color{green}{q}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{9}q-\frac{4}{13}q+\frac{4}{13}.\frac{11}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{9})+(\frac{-4}{13}))q+\frac{44}{117} & \text{Neem samen} \\ &=q^2-\frac{179}{117}q+\frac{44}{117} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{6}-x)(a-\frac{13}{4})& =(\color{red}{-x}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{4}x-\frac{3}{2}a+\frac{3}{2}.\frac{13}{4}& \text{Uitwerken } \\ & =-ax+\frac{13}{4}x-\frac{3}{2}a+\frac{39}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{14}+x)(q+\frac{-16}{16})& =(\color{red}{x}+\color{orange}{\frac{-2}{7}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-\frac{2}{7}q+\frac{2}{7}.1& \text{Uitwerken } \\ & =qx-1x-\frac{2}{7}q+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{12}{16})(\frac{17}{6}-a)& =(\color{red}{b}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{6}b-\frac{3}{4}a+\frac{3}{4}.\frac{17}{6}& \text{Uitwerken } \\ & =-ab+\frac{17}{6}b-\frac{3}{4}a+\frac{51}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{17}{6}b-\frac{3}{4}a+\frac{17}{8} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{3}{10})(\frac{13}{6}-p)& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{-p}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{6}x+\frac{3}{10}p-\frac{3}{10}.\frac{13}{6}& \text{Uitwerken } \\ & =-px+\frac{13}{6}x+\frac{3}{10}p-\frac{39}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{13}{6}x+\frac{3}{10}p-\frac{13}{20} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{15}-a)(b-\frac{9}{13})& =(\color{red}{-a}+\color{orange}{\frac{4}{15}}).(\color{green}{b}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{4}{15})} . \color{green}{(b)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{9}{13}a+\frac{4}{15}b-\frac{4}{15}.\frac{9}{13}& \text{Uitwerken } \\ & =-ab+\frac{9}{13}a+\frac{4}{15}b-\frac{36}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{9}{13}a+\frac{4}{15}b-\frac{12}{65} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{18}-a)(\frac{-14}{18}+q)& =(\color{red}{-a}+\color{orange}{\frac{1}{9}}).(\color{green}{q}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{9}a+\frac{1}{9}q-\frac{1}{9}.\frac{7}{9}& \text{Uitwerken } \\ & =-aq+\frac{7}{9}a+\frac{1}{9}q-\frac{7}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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