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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-7}{19})(\frac{-5}{14}+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{19}}).(\color{green}{p}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{14}p-\frac{7}{19}p+\frac{7}{19}.\frac{5}{14}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{14})+(\frac{-7}{19}))p+\frac{35}{266} & \text{Neem samen} \\ &=p^2-\frac{193}{266}p+\frac{35}{266} & \text{Maak de som} \\ &=p^2-\frac{193}{266}p+\frac{5}{38} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{20}-q)(q-\frac{7}{16})& =(\color{red}{-q}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{7}{16}q+\frac{2}{5}q-\frac{2}{5}.\frac{7}{16}& \text{Uitwerken } \\ & =-q^2+(\frac{7}{16}+\frac{2}{5})q-\frac{14}{80} & \text{Neem samen} \\ &=-q^2+\frac{67}{80}q-\frac{14}{80} & \text{Maak de som} \\ &=-q^2+\frac{67}{80}q-\frac{7}{40} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(a+\frac{14}{16})(q-11)& =(\color{red}{a}+\color{orange}{\frac{7}{8}}).(\color{green}{q}+\color{blue}{(-11)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-11)} + \color{orange}{(\frac{7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = aq-11a+\frac{7}{8}q-\frac{7}{8}.11& \text{Uitwerken } \\ & =aq-11a+\frac{7}{8}q-\frac{77}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-13}{8})(b-\frac{19}{15})& =(\color{red}{q}+\color{orange}{\frac{13}{8}}).(\color{green}{b}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{13}{8})} . \color{green}{(b)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{15}q+\frac{13}{8}b-\frac{13}{8}.\frac{19}{15}& \text{Uitwerken } \\ & =bq-\frac{19}{15}q+\frac{13}{8}b-\frac{247}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{12}-a)(\frac{-20}{14}-b)& =(\color{red}{-a}+\color{orange}{\frac{5}{3}}).(\color{green}{-b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{10}{7}a-\frac{5}{3}b-\frac{5}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =ab+\frac{10}{7}a-\frac{5}{3}b-\frac{50}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{4}+a)(\frac{5}{18}-b)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{-b}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{18}a-\frac{3}{2}b+\frac{3}{2}.\frac{5}{18}& \text{Uitwerken } \\ & =-ab+\frac{5}{18}a-\frac{3}{2}b+\frac{15}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{18}a-\frac{3}{2}b+\frac{5}{12} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{15}-q)(a-\frac{3}{19})& =(\color{red}{-q}+\color{orange}{\frac{-2}{15}}).(\color{green}{a}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{19}q-\frac{2}{15}a+\frac{2}{15}.\frac{3}{19}& \text{Uitwerken } \\ & =-aq+\frac{3}{19}q-\frac{2}{15}a+\frac{6}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{3}{19}q-\frac{2}{15}a+\frac{2}{95} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{20}{20}-x)(p+\frac{17}{19})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{19}x+1p+1.\frac{17}{19}& \text{Uitwerken } \\ & =-px-\frac{17}{19}x+1p+\frac{17}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{9}{16})(\frac{-9}{17}-p)& =(\color{red}{p}+\color{orange}{\frac{-9}{16}}).(\color{green}{-p}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{9}{17}p+\frac{9}{16}p+\frac{9}{16}.\frac{9}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-9}{17})+\frac{9}{16})p+(\frac{-81}{272}) & \text{Neem samen} \\ &=-p^2+\frac{9}{272}p+(\frac{-81}{272}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{11}+x)(x-\frac{10}{7})& =(\color{red}{x}+\color{orange}{\frac{15}{11}}).(\color{green}{x}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{15}{11})} . \color{green}{(x)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{10}{7}x+\frac{15}{11}x-\frac{15}{11}.\frac{10}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-10}{7})+\frac{15}{11})x-(\frac{-150}{77}) & \text{Neem samen} \\ &=x^2-\frac{5}{77}x-(\frac{-150}{77}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p+\frac{4}{2})((-7)-p)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-7)} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -pp-7p-2p-2.7& \text{Uitwerken } \\ & =-p^2+((-7)+(-2))p-14 & \text{Neem samen} \\ &=-p^2-9p-14 & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{14}+b)(\frac{17}{3}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{14}}).(\color{green}{b}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{17}{3}b-\frac{9}{14}b-\frac{9}{14}.\frac{17}{3}& \text{Uitwerken } \\ & =b^2+(\frac{17}{3}+(\frac{-9}{14}))b-(\frac{-153}{42}) & \text{Neem samen} \\ &=b^2+\frac{211}{42}b-(\frac{-153}{42}) & \text{Maak de som} \\ &=b^2+\frac{211}{42}b+\frac{51}{14} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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