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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{18}{7})(a+\frac{2}{12})& =(\color{red}{q}+\color{orange}{\frac{-18}{7}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{6}q-\frac{18}{7}a-\frac{18}{7}.\frac{1}{6}& \text{Uitwerken } \\ & =aq+\frac{1}{6}q-\frac{18}{7}a-\frac{18}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{6}q-\frac{18}{7}a-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-1}{10}+b)(q-\frac{-11}{5})& =(\color{red}{b}+\color{orange}{\frac{-1}{10}}).(\color{green}{q}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{5}b-\frac{1}{10}q-\frac{1}{10}.\frac{11}{5}& \text{Uitwerken } \\ & =bq+\frac{11}{5}b-\frac{1}{10}q-\frac{11}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{14}{5})(\frac{7}{19}+b)& =(\color{red}{x}+\color{orange}{\frac{-14}{5}}).(\color{green}{b}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{19}x-\frac{14}{5}b-\frac{14}{5}.\frac{7}{19}& \text{Uitwerken } \\ & =bx+\frac{7}{19}x-\frac{14}{5}b-\frac{98}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{-17}{11})(p+\frac{-1}{2})& =(\color{red}{x}+\color{orange}{\frac{-17}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{2}x-\frac{17}{11}p+\frac{17}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =px-\frac{1}{2}x-\frac{17}{11}p+\frac{17}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{8}{3})(\frac{15}{7}-x)& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{-x}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{15}{7}q-\frac{8}{3}x+\frac{8}{3}.\frac{15}{7}& \text{Uitwerken } \\ & =-qx+\frac{15}{7}q-\frac{8}{3}x+\frac{120}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{15}{7}q-\frac{8}{3}x+\frac{40}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{-5}{3})(\frac{-10}{13}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{13}x+\frac{5}{3}a-\frac{5}{3}.\frac{10}{13}& \text{Uitwerken } \\ & =ax-\frac{10}{13}x+\frac{5}{3}a-\frac{50}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-19}{11}-q)(x+16)& =(\color{red}{-q}+\color{orange}{\frac{-19}{11}}).(\color{green}{x}+\color{blue}{16})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(16)} + \color{orange}{(\frac{-19}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = -qx-16q-\frac{19}{11}x-\frac{19}{11}.16& \text{Uitwerken } \\ & =-qx-16q-\frac{19}{11}x-\frac{304}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{5}{3}-b)(\frac{-1}{19}-q)& =(\color{red}{-b}+\color{orange}{\frac{5}{3}}).(\color{green}{-q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{19}b-\frac{5}{3}q-\frac{5}{3}.\frac{1}{19}& \text{Uitwerken } \\ & =bq+\frac{1}{19}b-\frac{5}{3}q-\frac{5}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{-11}{14})(b-\frac{17}{17})& =(\color{red}{b}+\color{orange}{\frac{11}{14}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{14})} . \color{green}{(b)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bb-1b+\frac{11}{14}b-\frac{11}{14}.1& \text{Uitwerken } \\ & =b^2+((-1)+\frac{11}{14})b-(\frac{-11}{14}) & \text{Neem samen} \\ &=b^2-\frac{3}{14}b-(\frac{-11}{14}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(q-\frac{16}{18})(\frac{-19}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{-8}{9}}).(\color{green}{-a}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{6}q+\frac{8}{9}a+\frac{8}{9}.\frac{19}{6}& \text{Uitwerken } \\ & =-aq-\frac{19}{6}q+\frac{8}{9}a+\frac{152}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{19}{6}q+\frac{8}{9}a+\frac{76}{27} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-6}{11}-p)(\frac{-18}{7}-x)& =(\color{red}{-p}+\color{orange}{\frac{-6}{11}}).(\color{green}{-x}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{18}{7}p+\frac{6}{11}x+\frac{6}{11}.\frac{18}{7}& \text{Uitwerken } \\ & =px+\frac{18}{7}p+\frac{6}{11}x+\frac{108}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{7}{3})(q-\frac{1}{11})& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{11}p-\frac{7}{3}q+\frac{7}{3}.\frac{1}{11}& \text{Uitwerken } \\ & =pq-\frac{1}{11}p-\frac{7}{3}q+\frac{7}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)