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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-19}{20})(\frac{12}{2}-b)& =(\color{red}{x}+\color{orange}{\frac{-19}{20}}).(\color{green}{-b}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -bx+6x+\frac{19}{20}b-\frac{19}{20}.6& \text{Uitwerken } \\ & =-bx+6x+\frac{19}{20}b-\frac{114}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+6x+\frac{19}{20}b-\frac{57}{10} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{14}+q)(a-\frac{12}{8})& =(\color{red}{q}+\color{orange}{\frac{11}{14}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{11}{14})} . \color{green}{(a)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{2}q+\frac{11}{14}a-\frac{11}{14}.\frac{3}{2}& \text{Uitwerken } \\ & =aq-\frac{3}{2}q+\frac{11}{14}a-\frac{33}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{13}-b)(x-\frac{-19}{17})& =(\color{red}{-b}+\color{orange}{\frac{-14}{13}}).(\color{green}{x}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{17}b-\frac{14}{13}x-\frac{14}{13}.\frac{19}{17}& \text{Uitwerken } \\ & =-bx-\frac{19}{17}b-\frac{14}{13}x-\frac{266}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{5}{12})(p-\frac{-14}{8})& =(\color{red}{b}+\color{orange}{\frac{-5}{12}}).(\color{green}{p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{4}b-\frac{5}{12}p-\frac{5}{12}.\frac{7}{4}& \text{Uitwerken } \\ & =bp+\frac{7}{4}b-\frac{5}{12}p-\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-11}{17})(b+\frac{-1}{11})& =(\color{red}{x}+\color{orange}{\frac{11}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{11}{17})} . \color{green}{(b)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{11}x+\frac{11}{17}b-\frac{11}{17}.\frac{1}{11}& \text{Uitwerken } \\ & =bx-\frac{1}{11}x+\frac{11}{17}b-\frac{11}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{11}x+\frac{11}{17}b-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{7}{8})(\frac{-12}{14}+q)& =(\color{red}{q}+\color{orange}{\frac{-7}{8}}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{6}{7}q-\frac{7}{8}q+\frac{7}{8}.\frac{6}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-6}{7})+(\frac{-7}{8}))q+\frac{42}{56} & \text{Neem samen} \\ &=q^2-\frac{97}{56}q+\frac{42}{56} & \text{Maak de som} \\ &=q^2-\frac{97}{56}q+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(a-\frac{6}{13})(\frac{-4}{11}+a)& =(\color{red}{a}+\color{orange}{\frac{-6}{13}}).(\color{green}{a}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{11}a-\frac{6}{13}a+\frac{6}{13}.\frac{4}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{11})+(\frac{-6}{13}))a+\frac{24}{143} & \text{Neem samen} \\ &=a^2-\frac{118}{143}a+\frac{24}{143} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q+\frac{15}{14})(q+\frac{12}{4})& =(\color{red}{q}+\color{orange}{\frac{15}{14}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{15}{14})} . \color{green}{(q)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qq+3q+\frac{15}{14}q+\frac{15}{14}.3& \text{Uitwerken } \\ & =q^2+(3+\frac{15}{14})q+\frac{45}{14} & \text{Neem samen} \\ &=q^2+\frac{57}{14}q+\frac{45}{14} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{7}-p)(\frac{-16}{20}+q)& =(\color{red}{-p}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{4}{5}p-2q+2.\frac{4}{5}& \text{Uitwerken } \\ & =-pq+\frac{4}{5}p-2q+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{9}{14})(\frac{12}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{-9}{14}}).(\color{green}{a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{12}{7}p-\frac{9}{14}a-\frac{9}{14}.\frac{12}{7}& \text{Uitwerken } \\ & =ap+\frac{12}{7}p-\frac{9}{14}a-\frac{108}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{12}{7}p-\frac{9}{14}a-\frac{54}{49} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{15}{15})(p+\frac{3}{10})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{10}b+1p+1.\frac{3}{10}& \text{Uitwerken } \\ & =bp+\frac{3}{10}b+1p+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-9}{8})(b-\frac{10}{11})& =(\color{red}{q}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{10}{11}q+\frac{9}{8}b-\frac{9}{8}.\frac{10}{11}& \text{Uitwerken } \\ & =bq-\frac{10}{11}q+\frac{9}{8}b-\frac{90}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{10}{11}q+\frac{9}{8}b-\frac{45}{44} & \text{Vereenvoudig} \\\end{align}\)
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