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

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Werk uit en vereenvoudig

1. \((\frac{-15}{7}+b)(\frac{-19}{17}+x)\)
2. \((a+\frac{-14}{15})(x-\frac{7}{4})\)
3. \((p-\frac{18}{8})(x-\frac{-11}{17})\)
4. \((a-\frac{-4}{10})(q+\frac{-11}{12})\)
5. \((x+\frac{-11}{13})(\frac{19}{5}+x)\)
6. \((p+\frac{-14}{3})(b+\frac{13}{14})\)
7. \((b-\frac{5}{6})(p-\frac{-7}{16})\)
8. \((\frac{11}{6}+p)(p+\frac{1}{19})\)
9. \((p+\frac{6}{6})(\frac{-15}{17}+x)\)
10. \((a+\frac{8}{12})(p+\frac{2}{5})\)
11. \((\frac{18}{18}+q)(x-\frac{16}{6})\)
12. \((\frac{-8}{3}+p)(\frac{-20}{4}-q)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{7}+b)(\frac{-19}{17}+x)& =(\color{red}{b}+\color{orange}{\frac{-15}{7}}).(\color{green}{x}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{17}b-\frac{15}{7}x+\frac{15}{7}.\frac{19}{17}& \text{Uitwerken } \\ & =bx-\frac{19}{17}b-\frac{15}{7}x+\frac{285}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{-14}{15})(x-\frac{7}{4})& =(\color{red}{a}+\color{orange}{\frac{-14}{15}}).(\color{green}{x}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{4}a-\frac{14}{15}x+\frac{14}{15}.\frac{7}{4}& \text{Uitwerken } \\ & =ax-\frac{7}{4}a-\frac{14}{15}x+\frac{98}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{7}{4}a-\frac{14}{15}x+\frac{49}{30} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p-\frac{18}{8})(x-\frac{-11}{17})& =(\color{red}{p}+\color{orange}{\frac{-9}{4}}).(\color{green}{x}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{17}p-\frac{9}{4}x-\frac{9}{4}.\frac{11}{17}& \text{Uitwerken } \\ & =px+\frac{11}{17}p-\frac{9}{4}x-\frac{99}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{-4}{10})(q+\frac{-11}{12})& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{12}a+\frac{2}{5}q-\frac{2}{5}.\frac{11}{12}& \text{Uitwerken } \\ & =aq-\frac{11}{12}a+\frac{2}{5}q-\frac{22}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{11}{12}a+\frac{2}{5}q-\frac{11}{30} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{-11}{13})(\frac{19}{5}+x)& =(\color{red}{x}+\color{orange}{\frac{-11}{13}}).(\color{green}{x}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{19}{5}x-\frac{11}{13}x-\frac{11}{13}.\frac{19}{5}& \text{Uitwerken } \\ & =x^2+(\frac{19}{5}+(\frac{-11}{13}))x-(\frac{-209}{65}) & \text{Neem samen} \\ &=x^2+\frac{192}{65}x-(\frac{-209}{65}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(p+\frac{-14}{3})(b+\frac{13}{14})& =(\color{red}{p}+\color{orange}{\frac{-14}{3}}).(\color{green}{b}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{14}p-\frac{14}{3}b-\frac{14}{3}.\frac{13}{14}& \text{Uitwerken } \\ & =bp+\frac{13}{14}p-\frac{14}{3}b-\frac{182}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{14}p-\frac{14}{3}b-\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{5}{6})(p-\frac{-7}{16})& =(\color{red}{b}+\color{orange}{\frac{-5}{6}}).(\color{green}{p}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{16}b-\frac{5}{6}p-\frac{5}{6}.\frac{7}{16}& \text{Uitwerken } \\ & =bp+\frac{7}{16}b-\frac{5}{6}p-\frac{35}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{11}{6}+p)(p+\frac{1}{19})& =(\color{red}{p}+\color{orange}{\frac{11}{6}}).(\color{green}{p}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{11}{6})} . \color{green}{(p)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{19}p+\frac{11}{6}p+\frac{11}{6}.\frac{1}{19}& \text{Uitwerken } \\ & =p^2+(\frac{1}{19}+\frac{11}{6})p+\frac{11}{114} & \text{Neem samen} \\ &=p^2+\frac{215}{114}p+\frac{11}{114} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(p+\frac{6}{6})(\frac{-15}{17}+x)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{15}{17}p+1x-1.\frac{15}{17}& \text{Uitwerken } \\ & =px-\frac{15}{17}p+1x-\frac{15}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{8}{12})(p+\frac{2}{5})& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{5}a+\frac{2}{3}p+\frac{2}{3}.\frac{2}{5}& \text{Uitwerken } \\ & =ap+\frac{2}{5}a+\frac{2}{3}p+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{18}{18}+q)(x-\frac{16}{6})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{3}q+1x-1.\frac{8}{3}& \text{Uitwerken } \\ & =qx-\frac{8}{3}q+1x-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-8}{3}+p)(\frac{-20}{4}-q)& =(\color{red}{p}+\color{orange}{\frac{-8}{3}}).(\color{green}{-q}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -pq-5p+\frac{8}{3}q+\frac{8}{3}.5& \text{Uitwerken } \\ & =-pq-5p+\frac{8}{3}q+\frac{40}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)