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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{16}-x)(a-\frac{14}{16})& =(\color{red}{-x}+\color{orange}{\frac{-3}{8}}).(\color{green}{a}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{8}x-\frac{3}{8}a+\frac{3}{8}.\frac{7}{8}& \text{Uitwerken } \\ & =-ax+\frac{7}{8}x-\frac{3}{8}a+\frac{21}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-16}{12}-a)(p-\frac{-15}{15})& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1a-\frac{4}{3}p-\frac{4}{3}.1& \text{Uitwerken } \\ & =-ap-1a-\frac{4}{3}p-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{9}+b)(x+\frac{10}{4})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{2}b-\frac{2}{3}x-\frac{2}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =bx+\frac{5}{2}b-\frac{2}{3}x-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{2}b-\frac{2}{3}x-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-\frac{14}{9})(b+\frac{-5}{4})& =(\color{red}{x}+\color{orange}{\frac{-14}{9}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{4}x-\frac{14}{9}b+\frac{14}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =bx-\frac{5}{4}x-\frac{14}{9}b+\frac{70}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{5}{4}x-\frac{14}{9}b+\frac{35}{18} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{17}-p)(p+\frac{-15}{11})& =(\color{red}{-p}+\color{orange}{\frac{-10}{17}}).(\color{green}{p}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{15}{11}p-\frac{10}{17}p+\frac{10}{17}.\frac{15}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{15}{11}+(\frac{-10}{17}))p+(\frac{-150}{187}) & \text{Neem samen} \\ &=-p^2+\frac{145}{187}p+(\frac{-150}{187}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a+\frac{16}{16})(\frac{-11}{15}-b)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{11}{15}a-1b-1.\frac{11}{15}& \text{Uitwerken } \\ & =-ab-\frac{11}{15}a-1b-\frac{11}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{16}+q)(\frac{-15}{7}-x)& =(\color{red}{q}+\color{orange}{\frac{-17}{16}}).(\color{green}{-x}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{15}{7}q+\frac{17}{16}x+\frac{17}{16}.\frac{15}{7}& \text{Uitwerken } \\ & =-qx-\frac{15}{7}q+\frac{17}{16}x+\frac{255}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-7}{19}+x)(x-\frac{-15}{5})& =(\color{red}{x}+\color{orange}{\frac{-7}{19}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{-7}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = xx+3x-\frac{7}{19}x-\frac{7}{19}.3& \text{Uitwerken } \\ & =x^2+(3+(\frac{-7}{19}))x-(\frac{-21}{19}) & \text{Neem samen} \\ &=x^2+\frac{50}{19}x-(\frac{-21}{19}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(p-9)(b-\frac{6}{7})& =(\color{red}{p}+\color{orange}{(-9)}).(\color{green}{b}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(-9)} . \color{green}{(b)} + \color{orange}{(-9)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{7}p-9b+9.\frac{6}{7}& \text{Uitwerken } \\ & =bp-\frac{6}{7}p-9b+\frac{54}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{13}+p)(b-\frac{13}{9})& =(\color{red}{p}+\color{orange}{\frac{-15}{13}}).(\color{green}{b}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{9}p-\frac{15}{13}b+\frac{15}{13}.\frac{13}{9}& \text{Uitwerken } \\ & =bp-\frac{13}{9}p-\frac{15}{13}b+\frac{195}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{13}{9}p-\frac{15}{13}b+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{6}-x)(\frac{5}{16}-p)& =(\color{red}{-x}+\color{orange}{\frac{-4}{3}}).(\color{green}{-p}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{16}x+\frac{4}{3}p-\frac{4}{3}.\frac{5}{16}& \text{Uitwerken } \\ & =px-\frac{5}{16}x+\frac{4}{3}p-\frac{20}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{16}x+\frac{4}{3}p-\frac{5}{12} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{6}+p)(\frac{-12}{18}+q)& =(\color{red}{p}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{3}p-\frac{5}{6}q+\frac{5}{6}.\frac{2}{3}& \text{Uitwerken } \\ & =pq-\frac{2}{3}p-\frac{5}{6}q+\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{3}p-\frac{5}{6}q+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-14 04:52:02