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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{18}{6})(p-\frac{8}{7})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{7}a-3p+3.\frac{8}{7}& \text{Uitwerken } \\ & =ap-\frac{8}{7}a-3p+\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{12}-x)(x-\frac{-20}{6})& =(\color{red}{-x}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{10}{3}x+\frac{1}{4}x+\frac{1}{4}.\frac{10}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-10}{3})+\frac{1}{4})x+(\frac{-10}{12}) & \text{Neem samen} \\ &=-x^2-\frac{37}{12}x+(\frac{-10}{12}) & \text{Maak de som} \\ &=-x^2-\frac{37}{12}x+(\frac{-5}{6}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{20}+a)(\frac{1}{3}-b)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{-b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{3}a-\frac{4}{5}b+\frac{4}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =-ab+\frac{1}{3}a-\frac{4}{5}b+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{10}+q)(p-\frac{-14}{5})& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{p}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{9}{10})} . \color{green}{(p)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{14}{5}q+\frac{9}{10}p+\frac{9}{10}.\frac{14}{5}& \text{Uitwerken } \\ & =pq+\frac{14}{5}q+\frac{9}{10}p+\frac{126}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{14}{5}q+\frac{9}{10}p+\frac{63}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{17}{6})(x-\frac{10}{11})& =(\color{red}{x}+\color{orange}{\frac{-17}{6}}).(\color{green}{x}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{10}{11}x-\frac{17}{6}x+\frac{17}{6}.\frac{10}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-10}{11})+(\frac{-17}{6}))x+\frac{170}{66} & \text{Neem samen} \\ &=x^2-\frac{247}{66}x+\frac{170}{66} & \text{Maak de som} \\ &=x^2-\frac{247}{66}x+\frac{85}{33} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{17}-p)(\frac{15}{16}+p)& =(\color{red}{-p}+\color{orange}{\frac{18}{17}}).(\color{green}{p}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{18}{17})} . \color{green}{(p)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{15}{16}p+\frac{18}{17}p+\frac{18}{17}.\frac{15}{16}& \text{Uitwerken } \\ & =-p^2+((\frac{-15}{16})+\frac{18}{17})p+(\frac{-270}{272}) & \text{Neem samen} \\ &=-p^2+\frac{33}{272}p+(\frac{-270}{272}) & \text{Maak de som} \\ &=-p^2+\frac{33}{272}p+(\frac{-135}{136}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{6}-a)(a-15)& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{a}+\color{blue}{(-15)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(-15)} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -aa+15a+2a-2.15& \text{Uitwerken } \\ & =-a^2+(15+2)a-30 & \text{Neem samen} \\ &=-a^2+17a-30 & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{9}+q)(a-\frac{-7}{20})& =(\color{red}{q}+\color{orange}{\frac{-1}{9}}).(\color{green}{a}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{20}q-\frac{1}{9}a-\frac{1}{9}.\frac{7}{20}& \text{Uitwerken } \\ & =aq+\frac{7}{20}q-\frac{1}{9}a-\frac{7}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{3}{8})(q-\frac{16}{2})& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{q}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-8)} + \color{orange}{(\frac{3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = bq-8b+\frac{3}{8}q-\frac{3}{8}.8& \text{Uitwerken } \\ & =bq-8b+\frac{3}{8}q-\frac{24}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-8b+\frac{3}{8}q-3 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-17)(q-\frac{-15}{8})& =(\color{red}{b}+\color{orange}{(-17)}).(\color{green}{q}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(-17)} . \color{green}{(q)} + \color{orange}{(-17)} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{8}b-17q-17.\frac{15}{8}& \text{Uitwerken } \\ & =bq+\frac{15}{8}b-17q-\frac{255}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-2}{10})(p+\frac{-6}{2})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp-3b+\frac{1}{5}p-\frac{1}{5}.3& \text{Uitwerken } \\ & =bp-3b+\frac{1}{5}p-\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-16}{14}-p)(x-\frac{-12}{20})& =(\color{red}{-p}+\color{orange}{\frac{-8}{7}}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{5}p-\frac{8}{7}x-\frac{8}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =-px-\frac{3}{5}p-\frac{8}{7}x-\frac{24}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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