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

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  1. \((\frac{16}{4}-q)(\frac{-14}{8}-a)\)
  2. \((a-\frac{-6}{4})(\frac{-12}{19}-x)\)
  3. \((\frac{9}{19}+b)(\frac{-7}{10}-p)\)
  4. \((q+\frac{-4}{13})(p-\frac{17}{8})\)
  5. \((\frac{12}{19}-q)(\frac{-12}{18}-p)\)
  6. \((b+\frac{17}{18})(q-\frac{-8}{11})\)
  7. \((\frac{14}{5}+p)(\frac{15}{8}+q)\)
  8. \((a+\frac{-4}{19})(\frac{5}{20}+a)\)
  9. \((b+\frac{-13}{17})(\frac{20}{2}+p)\)
  10. \((\frac{15}{12}+a)(b+19)\)
  11. \((p+\frac{9}{13})(\frac{-4}{3}-x)\)
  12. \((\frac{-15}{3}+a)(b+\frac{-15}{5})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{4}-q)(\frac{-14}{8}-a)& =(\color{red}{-q}+\color{orange}{4}).(\color{green}{-a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(4)} . \color{green}{(-a)} + \color{orange}{(4)} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{4}q-4a-4.\frac{7}{4}& \text{Uitwerken } \\ & =aq+\frac{7}{4}q-4a-\frac{28}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{7}{4}q-4a-7 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-6}{4})(\frac{-12}{19}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{12}{19}a-\frac{3}{2}x-\frac{3}{2}.\frac{12}{19}& \text{Uitwerken } \\ & =-ax-\frac{12}{19}a-\frac{3}{2}x-\frac{36}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{12}{19}a-\frac{3}{2}x-\frac{18}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{9}{19}+b)(\frac{-7}{10}-p)& =(\color{red}{b}+\color{orange}{\frac{9}{19}}).(\color{green}{-p}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{9}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{10}b-\frac{9}{19}p-\frac{9}{19}.\frac{7}{10}& \text{Uitwerken } \\ & =-bp-\frac{7}{10}b-\frac{9}{19}p-\frac{63}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-4}{13})(p-\frac{17}{8})& =(\color{red}{q}+\color{orange}{\frac{-4}{13}}).(\color{green}{p}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{8}q-\frac{4}{13}p+\frac{4}{13}.\frac{17}{8}& \text{Uitwerken } \\ & =pq-\frac{17}{8}q-\frac{4}{13}p+\frac{68}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{17}{8}q-\frac{4}{13}p+\frac{17}{26} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{19}-q)(\frac{-12}{18}-p)& =(\color{red}{-q}+\color{orange}{\frac{12}{19}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{12}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{3}q-\frac{12}{19}p-\frac{12}{19}.\frac{2}{3}& \text{Uitwerken } \\ & =pq+\frac{2}{3}q-\frac{12}{19}p-\frac{24}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{2}{3}q-\frac{12}{19}p-\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{17}{18})(q-\frac{-8}{11})& =(\color{red}{b}+\color{orange}{\frac{17}{18}}).(\color{green}{q}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{17}{18})} . \color{green}{(q)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{11}b+\frac{17}{18}q+\frac{17}{18}.\frac{8}{11}& \text{Uitwerken } \\ & =bq+\frac{8}{11}b+\frac{17}{18}q+\frac{136}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{8}{11}b+\frac{17}{18}q+\frac{68}{99} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{14}{5}+p)(\frac{15}{8}+q)& =(\color{red}{p}+\color{orange}{\frac{14}{5}}).(\color{green}{q}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{14}{5})} . \color{green}{(q)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{8}p+\frac{14}{5}q+\frac{14}{5}.\frac{15}{8}& \text{Uitwerken } \\ & =pq+\frac{15}{8}p+\frac{14}{5}q+\frac{210}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{15}{8}p+\frac{14}{5}q+\frac{21}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-4}{19})(\frac{5}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{-4}{19}}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{4}a-\frac{4}{19}a-\frac{4}{19}.\frac{1}{4}& \text{Uitwerken } \\ & =a^2+(\frac{1}{4}+(\frac{-4}{19}))a-(\frac{-4}{76}) & \text{Neem samen} \\ &=a^2+\frac{3}{76}a-(\frac{-4}{76}) & \text{Maak de som} \\ &=a^2+\frac{3}{76}a+\frac{1}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-13}{17})(\frac{20}{2}+p)& =(\color{red}{b}+\color{orange}{\frac{-13}{17}}).(\color{green}{p}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(10)} + \color{orange}{(\frac{-13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = bp+10b-\frac{13}{17}p-\frac{13}{17}.10& \text{Uitwerken } \\ & =bp+10b-\frac{13}{17}p-\frac{130}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{12}+a)(b+19)& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{19})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(19)} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = ab+19a+\frac{5}{4}b+\frac{5}{4}.19& \text{Uitwerken } \\ & =ab+19a+\frac{5}{4}b+\frac{95}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{9}{13})(\frac{-4}{3}-x)& =(\color{red}{p}+\color{orange}{\frac{9}{13}}).(\color{green}{-x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{9}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{3}p-\frac{9}{13}x-\frac{9}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =-px-\frac{4}{3}p-\frac{9}{13}x-\frac{36}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{4}{3}p-\frac{9}{13}x-\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{3}+a)(b+\frac{-15}{5})& =(\color{red}{a}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ab-3a-5b+5.3& \text{Uitwerken } \\ & =ab-3a-5b+15 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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