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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-5}{8})(a+\frac{1}{9})& =(\color{red}{q}+\color{orange}{\frac{5}{8}}).(\color{green}{a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{9}q+\frac{5}{8}a+\frac{5}{8}.\frac{1}{9}& \text{Uitwerken } \\ & =aq+\frac{1}{9}q+\frac{5}{8}a+\frac{5}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{9}{11}+q)(b+\frac{-13}{3})& =(\color{red}{q}+\color{orange}{\frac{9}{11}}).(\color{green}{b}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{3}q+\frac{9}{11}b-\frac{9}{11}.\frac{13}{3}& \text{Uitwerken } \\ & =bq-\frac{13}{3}q+\frac{9}{11}b-\frac{117}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{3}q+\frac{9}{11}b-\frac{39}{11} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q-\frac{13}{6})(\frac{12}{14}-p)& =(\color{red}{q}+\color{orange}{\frac{-13}{6}}).(\color{green}{-p}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{6}{7}q+\frac{13}{6}p-\frac{13}{6}.\frac{6}{7}& \text{Uitwerken } \\ & =-pq+\frac{6}{7}q+\frac{13}{6}p-\frac{78}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{6}{7}q+\frac{13}{6}p-\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{3}{6}+q)(\frac{13}{17}+b)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{17}q+\frac{1}{2}b+\frac{1}{2}.\frac{13}{17}& \text{Uitwerken } \\ & =bq+\frac{13}{17}q+\frac{1}{2}b+\frac{13}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{12}-p)(b+\frac{12}{10})& =(\color{red}{-p}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{6}{5}p-\frac{4}{3}b-\frac{4}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =-bp-\frac{6}{5}p-\frac{4}{3}b-\frac{24}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{6}{5}p-\frac{4}{3}b-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x+\frac{-11}{18})(\frac{-5}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{-11}{18}}).(\color{green}{q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{3}x-\frac{11}{18}q+\frac{11}{18}.\frac{5}{3}& \text{Uitwerken } \\ & =qx-\frac{5}{3}x-\frac{11}{18}q+\frac{55}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-2}{8}-q)(b-\frac{17}{5})& =(\color{red}{-q}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{5}q-\frac{1}{4}b+\frac{1}{4}.\frac{17}{5}& \text{Uitwerken } \\ & =-bq+\frac{17}{5}q-\frac{1}{4}b+\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{4}{18})(\frac{-17}{17}-q)& =(\color{red}{q}+\color{orange}{\frac{2}{9}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q-\frac{2}{9}q-\frac{2}{9}.1& \text{Uitwerken } \\ & =-q^2+((-1)+(\frac{-2}{9}))q-\frac{2}{9} & \text{Neem samen} \\ &=-q^2-\frac{11}{9}q-\frac{2}{9} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(x+\frac{16}{17})(q+\frac{10}{9})& =(\color{red}{x}+\color{orange}{\frac{16}{17}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{16}{17})} . \color{green}{(q)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{10}{9}x+\frac{16}{17}q+\frac{16}{17}.\frac{10}{9}& \text{Uitwerken } \\ & =qx+\frac{10}{9}x+\frac{16}{17}q+\frac{160}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{18}{4}-x)(a-\frac{2}{14})& =(\color{red}{-x}+\color{orange}{\frac{9}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{9}{2})} . \color{green}{(a)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{7}x+\frac{9}{2}a-\frac{9}{2}.\frac{1}{7}& \text{Uitwerken } \\ & =-ax+\frac{1}{7}x+\frac{9}{2}a-\frac{9}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{6}{4}+q)(a-\frac{13}{18})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{18}q+\frac{3}{2}a-\frac{3}{2}.\frac{13}{18}& \text{Uitwerken } \\ & =aq-\frac{13}{18}q+\frac{3}{2}a-\frac{39}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{13}{18}q+\frac{3}{2}a-\frac{13}{12} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(p+9)(p-\frac{-1}{2})& =(\color{red}{p}+\color{orange}{9}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(9)} . \color{green}{(p)} + \color{orange}{(9)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{2}p+9p+9.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+(\frac{1}{2}+9)p+\frac{9}{2} & \text{Neem samen} \\ &=p^2+\frac{19}{2}p+\frac{9}{2} & \text{Maak de som} \\\end{align}\)