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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{4}-q)(q+(-10))& =(\color{red}{-q}+\color{orange}{\frac{-15}{4}}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-10)} + \color{orange}{(\frac{-15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -qq+10q-\frac{15}{4}q+\frac{15}{4}.10& \text{Uitwerken } \\ & =-q^2+(10+(\frac{-15}{4}))q+(\frac{-150}{4}) & \text{Neem samen} \\ &=-q^2+\frac{25}{4}q+(\frac{-150}{4}) & \text{Maak de som} \\ &=-q^2+\frac{25}{4}q+(\frac{-75}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-16}{9}+x)(p-\frac{-14}{8})& =(\color{red}{x}+\color{orange}{\frac{-16}{9}}).(\color{green}{p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{4}x-\frac{16}{9}p-\frac{16}{9}.\frac{7}{4}& \text{Uitwerken } \\ & =px+\frac{7}{4}x-\frac{16}{9}p-\frac{112}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{4}x-\frac{16}{9}p-\frac{28}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{10}{19}+x)(\frac{14}{12}-p)& =(\color{red}{x}+\color{orange}{\frac{10}{19}}).(\color{green}{-p}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{10}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{6}x-\frac{10}{19}p+\frac{10}{19}.\frac{7}{6}& \text{Uitwerken } \\ & =-px+\frac{7}{6}x-\frac{10}{19}p+\frac{70}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{7}{6}x-\frac{10}{19}p+\frac{35}{57} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{8}+x)(q+\frac{-12}{19})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{12}{19}x-1q+1.\frac{12}{19}& \text{Uitwerken } \\ & =qx-\frac{12}{19}x-1q+\frac{12}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+(-10))(a-\frac{14}{2})& =(\color{red}{b}+\color{orange}{(-10)}).(\color{green}{a}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-7)} + \color{orange}{(-10)} . \color{green}{(a)} + \color{orange}{(-10)} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = ab-7b-10a+10.7& \text{Uitwerken } \\ & =ab-7b-10a+70 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{11}-a)(q-16)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{(-16)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-16)} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = -aq+16a-1q+1.16& \text{Uitwerken } \\ & =-aq+16a-1q+16 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{8}-q)(q+\frac{19}{11})& =(\color{red}{-q}+\color{orange}{\frac{5}{2}}).(\color{green}{q}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{11}q+\frac{5}{2}q+\frac{5}{2}.\frac{19}{11}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{11})+\frac{5}{2})q+(\frac{-95}{22}) & \text{Neem samen} \\ &=-q^2+\frac{17}{22}q+(\frac{-95}{22}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p+\frac{10}{17})(\frac{17}{11}-q)& =(\color{red}{p}+\color{orange}{\frac{10}{17}}).(\color{green}{-q}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{10}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{11}p-\frac{10}{17}q+\frac{10}{17}.\frac{17}{11}& \text{Uitwerken } \\ & =-pq+\frac{17}{11}p-\frac{10}{17}q+\frac{170}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{17}{11}p-\frac{10}{17}q+\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{13}{11})(p-\frac{-18}{18})& =(\color{red}{b}+\color{orange}{\frac{-13}{11}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-13}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1b-\frac{13}{11}p-\frac{13}{11}.1& \text{Uitwerken } \\ & =bp+1b-\frac{13}{11}p-\frac{13}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-15}{12})(\frac{7}{7}+b)& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1a+\frac{5}{4}b+\frac{5}{4}.1& \text{Uitwerken } \\ & =ab+1a+\frac{5}{4}b+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-16}{7}+q)(\frac{14}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{-16}{7}}).(\color{green}{-q}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{14}{9}q+\frac{16}{7}q-\frac{16}{7}.\frac{14}{9}& \text{Uitwerken } \\ & =-q^2+(\frac{14}{9}+\frac{16}{7})q-\frac{224}{63} & \text{Neem samen} \\ &=-q^2+\frac{242}{63}q-\frac{224}{63} & \text{Maak de som} \\ &=-q^2+\frac{242}{63}q-\frac{32}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{16}-b)(\frac{6}{3}-a)& =(\color{red}{-b}+\color{orange}{\frac{19}{16}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(2)} + \color{orange}{(\frac{19}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b-\frac{19}{16}a+\frac{19}{16}.2& \text{Uitwerken } \\ & =ab-2b-\frac{19}{16}a+\frac{38}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-2b-\frac{19}{16}a+\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
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