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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{15}+x)((-8)+q)& =(\color{red}{x}+\color{orange}{\frac{16}{15}}).(\color{green}{q}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-8)} + \color{orange}{(\frac{16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = qx-8x+\frac{16}{15}q-\frac{16}{15}.8& \text{Uitwerken } \\ & =qx-8x+\frac{16}{15}q-\frac{128}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-1}{13}+p)(\frac{16}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{-1}{13}}).(\color{green}{a}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{7}p-\frac{1}{13}a-\frac{1}{13}.\frac{16}{7}& \text{Uitwerken } \\ & =ap+\frac{16}{7}p-\frac{1}{13}a-\frac{16}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-4}{13}+b)(p-\frac{8}{7})& =(\color{red}{b}+\color{orange}{\frac{-4}{13}}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{7}b-\frac{4}{13}p+\frac{4}{13}.\frac{8}{7}& \text{Uitwerken } \\ & =bp-\frac{8}{7}b-\frac{4}{13}p+\frac{32}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-(-19))(a+\frac{16}{19})& =(\color{red}{a}+\color{orange}{19}).(\color{green}{a}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(19)} . \color{green}{(a)} + \color{orange}{(19)} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{16}{19}a+19a+19.\frac{16}{19}& \text{Uitwerken } \\ & =a^2+(\frac{16}{19}+19)a+\frac{304}{19} & \text{Neem samen} \\ &=a^2+\frac{377}{19}a+\frac{304}{19} & \text{Maak de som} \\ &=a^2+\frac{377}{19}a+16 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{12}+x)(b-\frac{-15}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}x+\frac{1}{2}b+\frac{1}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}x+\frac{1}{2}b+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{17}{5})(p+\frac{-17}{16})& =(\color{red}{q}+\color{orange}{\frac{17}{5}}).(\color{green}{p}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{17}{5})} . \color{green}{(p)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{16}q+\frac{17}{5}p-\frac{17}{5}.\frac{17}{16}& \text{Uitwerken } \\ & =pq-\frac{17}{16}q+\frac{17}{5}p-\frac{289}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{2}-p)(\frac{-20}{2}+p)& =(\color{red}{-p}+\color{orange}{(-9)}).(\color{green}{p}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-10)} + \color{orange}{(-9)} . \color{green}{(p)} + \color{orange}{(-9)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -pp+10p-9p+9.10& \text{Uitwerken } \\ & =-p^2+(10+(-9))p+(-90) & \text{Neem samen} \\ &=-p^2+1p+(-90) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x-(-14))(a+\frac{12}{4})& =(\color{red}{x}+\color{orange}{14}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(14)} . \color{green}{(a)} + \color{orange}{(14)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ax+3x+14a+14.3& \text{Uitwerken } \\ & =ax+3x+14a+42 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-3}{5})(b+\frac{3}{20})& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{20}a+\frac{3}{5}b+\frac{3}{5}.\frac{3}{20}& \text{Uitwerken } \\ & =ab+\frac{3}{20}a+\frac{3}{5}b+\frac{9}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{5}-q)(a-\frac{-12}{9})& =(\color{red}{-q}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{4}{3}q-\frac{9}{5}a-\frac{9}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =-aq-\frac{4}{3}q-\frac{9}{5}a-\frac{36}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{4}{3}q-\frac{9}{5}a-\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{17}-a)(\frac{-5}{20}-q)& =(\color{red}{-a}+\color{orange}{\frac{-20}{17}}).(\color{green}{-q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{4}a+\frac{20}{17}q+\frac{20}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =aq+\frac{1}{4}a+\frac{20}{17}q+\frac{20}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{4}a+\frac{20}{17}q+\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{15}+a)(\frac{1}{16}-a)& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{-a}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{16}a-\frac{3}{5}a+\frac{3}{5}.\frac{1}{16}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{16}+(\frac{-3}{5}))a+(\frac{-3}{80}) & \text{Neem samen} \\ &=-a^2-\frac{43}{80}a+(\frac{-3}{80}) & \text{Maak de som} \\\end{align}\)
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