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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{5}{8})(\frac{14}{6}+b)& =(\color{red}{p}+\color{orange}{\frac{5}{8}}).(\color{green}{b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{3}p+\frac{5}{8}b+\frac{5}{8}.\frac{7}{3}& \text{Uitwerken } \\ & =bp+\frac{7}{3}p+\frac{5}{8}b+\frac{35}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{16}{17}-a)(b-\frac{13}{2})& =(\color{red}{-a}+\color{orange}{\frac{16}{17}}).(\color{green}{b}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{16}{17})} . \color{green}{(b)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{13}{2}a+\frac{16}{17}b-\frac{16}{17}.\frac{13}{2}& \text{Uitwerken } \\ & =-ab+\frac{13}{2}a+\frac{16}{17}b-\frac{208}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{13}{2}a+\frac{16}{17}b-\frac{104}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(9+q)(p-\frac{10}{10})& =(\color{red}{q}+\color{orange}{9}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(9)} . \color{green}{(p)} + \color{orange}{(9)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q+9p-9.1& \text{Uitwerken } \\ & =pq-1q+9p-9 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{10}{18})(\frac{-18}{8}-a)& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{-a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{4}q+\frac{5}{9}a+\frac{5}{9}.\frac{9}{4}& \text{Uitwerken } \\ & =-aq-\frac{9}{4}q+\frac{5}{9}a+\frac{45}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{9}{4}q+\frac{5}{9}a+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{8}-b)(a+\frac{13}{4})& =(\color{red}{-b}+\color{orange}{\frac{-9}{4}}).(\color{green}{a}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{13}{4}b-\frac{9}{4}a-\frac{9}{4}.\frac{13}{4}& \text{Uitwerken } \\ & =-ab-\frac{13}{4}b-\frac{9}{4}a-\frac{117}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{11}-p)(b+\frac{-18}{18})& =(\color{red}{-p}+\color{orange}{\frac{-14}{11}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1p-\frac{14}{11}b+\frac{14}{11}.1& \text{Uitwerken } \\ & =-bp+1p-\frac{14}{11}b+\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-6)(x-\frac{-8}{13})& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{x}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(-6)} . \color{green}{(x)} + \color{orange}{(-6)} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{13}a-6x-6.\frac{8}{13}& \text{Uitwerken } \\ & =ax+\frac{8}{13}a-6x-\frac{48}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{9}-q)(\frac{-5}{8}+p)& =(\color{red}{-q}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{8}q+\frac{4}{3}p-\frac{4}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =-pq+\frac{5}{8}q+\frac{4}{3}p-\frac{20}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{8}q+\frac{4}{3}p-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{7}-x)(\frac{1}{5}+x)& =(\color{red}{-x}+\color{orange}{\frac{5}{7}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{1}{5}x+\frac{5}{7}x+\frac{5}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =-x^2+((\frac{-1}{5})+\frac{5}{7})x+(\frac{-5}{35}) & \text{Neem samen} \\ &=-x^2+\frac{18}{35}x+(\frac{-5}{35}) & \text{Maak de som} \\ &=-x^2+\frac{18}{35}x+(\frac{-1}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(x+\frac{12}{12})(\frac{6}{4}+q)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}x+1q+1.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}x+1q+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{7}{11})(\frac{6}{5}-b)& =(\color{red}{a}+\color{orange}{\frac{-7}{11}}).(\color{green}{-b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{6}{5}a+\frac{7}{11}b-\frac{7}{11}.\frac{6}{5}& \text{Uitwerken } \\ & =-ab+\frac{6}{5}a+\frac{7}{11}b-\frac{42}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-12}{6})(\frac{-13}{16}+x)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{16}p+2x-2.\frac{13}{16}& \text{Uitwerken } \\ & =px-\frac{13}{16}p+2x-\frac{26}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{13}{16}p+2x-\frac{13}{8} & \text{Vereenvoudig} \\\end{align}\)
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