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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{15}+q)(a+\frac{-9}{9})& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1q-\frac{4}{3}a+\frac{4}{3}.1& \text{Uitwerken } \\ & =aq-1q-\frac{4}{3}a+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{8}{10}-b)(p-\frac{4}{13})& =(\color{red}{-b}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{4}{13}b+\frac{4}{5}p-\frac{4}{5}.\frac{4}{13}& \text{Uitwerken } \\ & =-bp+\frac{4}{13}b+\frac{4}{5}p-\frac{16}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{7}{18}-p)(p+\frac{17}{5})& =(\color{red}{-p}+\color{orange}{\frac{7}{18}}).(\color{green}{p}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{7}{18})} . \color{green}{(p)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{5}p+\frac{7}{18}p+\frac{7}{18}.\frac{17}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{5})+\frac{7}{18})p+(\frac{-119}{90}) & \text{Neem samen} \\ &=-p^2-\frac{271}{90}p+(\frac{-119}{90}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{15}{10}+q)(b+\frac{-19}{6})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{6}q+\frac{3}{2}b-\frac{3}{2}.\frac{19}{6}& \text{Uitwerken } \\ & =bq-\frac{19}{6}q+\frac{3}{2}b-\frac{57}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{19}{6}q+\frac{3}{2}b-\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-8}{4}+q)(x-\frac{14}{14})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q-2x+2.1& \text{Uitwerken } \\ & =qx-1q-2x+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{17}{18})(\frac{2}{17}+b)& =(\color{red}{x}+\color{orange}{\frac{-17}{18}}).(\color{green}{b}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{17}x-\frac{17}{18}b-\frac{17}{18}.\frac{2}{17}& \text{Uitwerken } \\ & =bx+\frac{2}{17}x-\frac{17}{18}b-\frac{34}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{2}{17}x-\frac{17}{18}b-\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x-\frac{1}{3})(\frac{-18}{10}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{-q}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{9}{5}x+\frac{1}{3}q+\frac{1}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =-qx-\frac{9}{5}x+\frac{1}{3}q+\frac{9}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{9}{5}x+\frac{1}{3}q+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}((-16)+x)(a+\frac{7}{16})& =(\color{red}{x}+\color{orange}{(-16)}).(\color{green}{a}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(-16)} . \color{green}{(a)} + \color{orange}{(-16)} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{16}x-16a-16.\frac{7}{16}& \text{Uitwerken } \\ & =ax+\frac{7}{16}x-16a-\frac{112}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{16}x-16a-7 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-16}{12}-b)(\frac{-12}{3}-b)& =(\color{red}{-b}+\color{orange}{\frac{-4}{3}}).(\color{green}{-b}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bb+4b+\frac{4}{3}b+\frac{4}{3}.4& \text{Uitwerken } \\ & =b^2+(4+\frac{4}{3})b+\frac{16}{3} & \text{Neem samen} \\ &=b^2+\frac{16}{3}b+\frac{16}{3} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p+\frac{17}{11})(\frac{-4}{16}-b)& =(\color{red}{p}+\color{orange}{\frac{17}{11}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{17}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{4}p-\frac{17}{11}b-\frac{17}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =-bp-\frac{1}{4}p-\frac{17}{11}b-\frac{17}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{6}{18}+b)(b-\frac{1}{17})& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{17}b+\frac{1}{3}b-\frac{1}{3}.\frac{1}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{17})+\frac{1}{3})b-(\frac{-1}{51}) & \text{Neem samen} \\ &=b^2+\frac{14}{51}b-(\frac{-1}{51}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(x+\frac{4}{12})(a-\frac{2}{6})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}x+\frac{1}{3}a-\frac{1}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}x+\frac{1}{3}a-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)