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

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  1. \((q-\frac{-14}{14})(\frac{-1}{4}+p)\)
  2. \((\frac{-12}{7}-p)(x+20)\)
  3. \((\frac{-16}{8}+q)(p-\frac{-6}{11})\)
  4. \((a-\frac{-19}{16})(a+\frac{-18}{11})\)
  5. \((\frac{-15}{2}-p)(\frac{-10}{18}-b)\)
  6. \((q+\frac{3}{4})(x-\frac{-6}{10})\)
  7. \((\frac{9}{16}+x)(19+x)\)
  8. \((\frac{4}{9}+q)(\frac{-8}{4}-q)\)
  9. \((\frac{-8}{8}-a)(p+\frac{-1}{7})\)
  10. \((b-\frac{15}{19})(\frac{7}{12}-q)\)
  11. \((a+\frac{-19}{12})(b-\frac{14}{13})\)
  12. \((q+\frac{-10}{3})(p-\frac{14}{18})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-14}{14})(\frac{-1}{4}+p)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{4}q+1p-1.\frac{1}{4}& \text{Uitwerken } \\ & =pq-\frac{1}{4}q+1p-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{7}-p)(x+20)& =(\color{red}{-p}+\color{orange}{\frac{-12}{7}}).(\color{green}{x}+\color{blue}{20})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(20)} + \color{orange}{(\frac{-12}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -px-20p-\frac{12}{7}x-\frac{12}{7}.20& \text{Uitwerken } \\ & =-px-20p-\frac{12}{7}x-\frac{240}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{8}+q)(p-\frac{-6}{11})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{11}q-2p-2.\frac{6}{11}& \text{Uitwerken } \\ & =pq+\frac{6}{11}q-2p-\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-19}{16})(a+\frac{-18}{11})& =(\color{red}{a}+\color{orange}{\frac{19}{16}}).(\color{green}{a}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{19}{16})} . \color{green}{(a)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{18}{11}a+\frac{19}{16}a-\frac{19}{16}.\frac{18}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-18}{11})+\frac{19}{16})a-(\frac{-342}{176}) & \text{Neem samen} \\ &=a^2-\frac{79}{176}a-(\frac{-342}{176}) & \text{Maak de som} \\ &=a^2-\frac{79}{176}a+\frac{171}{88} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{2}-p)(\frac{-10}{18}-b)& =(\color{red}{-p}+\color{orange}{\frac{-15}{2}}).(\color{green}{-b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{9}p+\frac{15}{2}b+\frac{15}{2}.\frac{5}{9}& \text{Uitwerken } \\ & =bp+\frac{5}{9}p+\frac{15}{2}b+\frac{75}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{9}p+\frac{15}{2}b+\frac{25}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{3}{4})(x-\frac{-6}{10})& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{5}q+\frac{3}{4}x+\frac{3}{4}.\frac{3}{5}& \text{Uitwerken } \\ & =qx+\frac{3}{5}q+\frac{3}{4}x+\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{16}+x)(19+x)& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{x}+\color{blue}{19})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(19)} + \color{orange}{(\frac{9}{16})} . \color{green}{(x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = xx+19x+\frac{9}{16}x+\frac{9}{16}.19& \text{Uitwerken } \\ & =x^2+(19+\frac{9}{16})x+\frac{171}{16} & \text{Neem samen} \\ &=x^2+\frac{313}{16}x+\frac{171}{16} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{9}+q)(\frac{-8}{4}-q)& =(\color{red}{q}+\color{orange}{\frac{4}{9}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{4}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -qq-2q-\frac{4}{9}q-\frac{4}{9}.2& \text{Uitwerken } \\ & =-q^2+((-2)+(\frac{-4}{9}))q-\frac{8}{9} & \text{Neem samen} \\ &=-q^2-\frac{22}{9}q-\frac{8}{9} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{8}-a)(p+\frac{-1}{7})& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{7}a-1p+1.\frac{1}{7}& \text{Uitwerken } \\ & =-ap+\frac{1}{7}a-1p+\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{15}{19})(\frac{7}{12}-q)& =(\color{red}{b}+\color{orange}{\frac{-15}{19}}).(\color{green}{-q}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{12}b+\frac{15}{19}q-\frac{15}{19}.\frac{7}{12}& \text{Uitwerken } \\ & =-bq+\frac{7}{12}b+\frac{15}{19}q-\frac{105}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{7}{12}b+\frac{15}{19}q-\frac{35}{76} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-19}{12})(b-\frac{14}{13})& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{b}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{14}{13}a-\frac{19}{12}b+\frac{19}{12}.\frac{14}{13}& \text{Uitwerken } \\ & =ab-\frac{14}{13}a-\frac{19}{12}b+\frac{266}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{14}{13}a-\frac{19}{12}b+\frac{133}{78} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-10}{3})(p-\frac{14}{18})& =(\color{red}{q}+\color{orange}{\frac{-10}{3}}).(\color{green}{p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{9}q-\frac{10}{3}p+\frac{10}{3}.\frac{7}{9}& \text{Uitwerken } \\ & =pq-\frac{7}{9}q-\frac{10}{3}p+\frac{70}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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