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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-3}{11}+p)(\frac{5}{5}+b)& =(\color{red}{p}+\color{orange}{\frac{-3}{11}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-3}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-\frac{3}{11}b-\frac{3}{11}.1& \text{Uitwerken } \\ & =bp+1p-\frac{3}{11}b-\frac{3}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{8}-b)(b-\frac{12}{17})& =(\color{red}{-b}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{12}{17}b-\frac{3}{8}b+\frac{3}{8}.\frac{12}{17}& \text{Uitwerken } \\ & =-b^2+(\frac{12}{17}+(\frac{-3}{8}))b+(\frac{-36}{136}) & \text{Neem samen} \\ &=-b^2+\frac{45}{136}b+(\frac{-36}{136}) & \text{Maak de som} \\ &=-b^2+\frac{45}{136}b+(\frac{-9}{34}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(a+\frac{15}{10})(\frac{9}{14}+p)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{14}a+\frac{3}{2}p+\frac{3}{2}.\frac{9}{14}& \text{Uitwerken } \\ & =ap+\frac{9}{14}a+\frac{3}{2}p+\frac{27}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-19}{18})(a-\frac{-5}{11})& =(\color{red}{b}+\color{orange}{\frac{19}{18}}).(\color{green}{a}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{19}{18})} . \color{green}{(a)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{11}b+\frac{19}{18}a+\frac{19}{18}.\frac{5}{11}& \text{Uitwerken } \\ & =ab+\frac{5}{11}b+\frac{19}{18}a+\frac{95}{198} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{14}-q)(a+\frac{-9}{8})& =(\color{red}{-q}+\color{orange}{\frac{9}{14}}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{9}{14})} . \color{green}{(a)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{8}q+\frac{9}{14}a-\frac{9}{14}.\frac{9}{8}& \text{Uitwerken } \\ & =-aq+\frac{9}{8}q+\frac{9}{14}a-\frac{81}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{10}{6})(q-\frac{20}{14})& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{7}a+\frac{5}{3}q-\frac{5}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =aq-\frac{10}{7}a+\frac{5}{3}q-\frac{50}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{7}+q)(\frac{15}{14}+q)& =(\color{red}{q}+\color{orange}{\frac{6}{7}}).(\color{green}{q}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{15}{14}q+\frac{6}{7}q+\frac{6}{7}.\frac{15}{14}& \text{Uitwerken } \\ & =q^2+(\frac{15}{14}+\frac{6}{7})q+\frac{90}{98} & \text{Neem samen} \\ &=q^2+\frac{27}{14}q+\frac{90}{98} & \text{Maak de som} \\ &=q^2+\frac{27}{14}q+\frac{45}{49} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-18}{10})(x-\frac{20}{17})& =(\color{red}{p}+\color{orange}{\frac{-9}{5}}).(\color{green}{x}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{20}{17}p-\frac{9}{5}x+\frac{9}{5}.\frac{20}{17}& \text{Uitwerken } \\ & =px-\frac{20}{17}p-\frac{9}{5}x+\frac{180}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{20}{17}p-\frac{9}{5}x+\frac{36}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{6}{2})(a+\frac{8}{6})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{3}b+3a+3.\frac{4}{3}& \text{Uitwerken } \\ & =ab+\frac{4}{3}b+3a+\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{4}{3}b+3a+4 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{18}-p)(\frac{-7}{4}+a)& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{4}p-\frac{1}{2}a+\frac{1}{2}.\frac{7}{4}& \text{Uitwerken } \\ & =-ap+\frac{7}{4}p-\frac{1}{2}a+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{8}-p)(\frac{19}{16}-b)& =(\color{red}{-p}+\color{orange}{\frac{-13}{8}}).(\color{green}{-b}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{16}p+\frac{13}{8}b-\frac{13}{8}.\frac{19}{16}& \text{Uitwerken } \\ & =bp-\frac{19}{16}p+\frac{13}{8}b-\frac{247}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(1-a)(a+\frac{-6}{7})& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{6}{7}a+1a-1.\frac{6}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{6}{7}+1)a-\frac{6}{7} & \text{Neem samen} \\ &=-a^2+\frac{13}{7}a-\frac{6}{7} & \text{Maak de som} \\\end{align}\)
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