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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-12}{5}-b)(q+\frac{5}{6})& =(\color{red}{-b}+\color{orange}{\frac{-12}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{6}b-\frac{12}{5}q-\frac{12}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-bq-\frac{5}{6}b-\frac{12}{5}q-\frac{60}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{6}b-\frac{12}{5}q-2 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-4}{18}+x)(q+\frac{-6}{11})& =(\color{red}{x}+\color{orange}{\frac{-2}{9}}).(\color{green}{q}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{11}x-\frac{2}{9}q+\frac{2}{9}.\frac{6}{11}& \text{Uitwerken } \\ & =qx-\frac{6}{11}x-\frac{2}{9}q+\frac{12}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{6}{11}x-\frac{2}{9}q+\frac{4}{33} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{11}+a)(a+\frac{-10}{8})& =(\color{red}{a}+\color{orange}{\frac{-10}{11}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{4}a-\frac{10}{11}a+\frac{10}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{4})+(\frac{-10}{11}))a+\frac{50}{44} & \text{Neem samen} \\ &=a^2-\frac{95}{44}a+\frac{50}{44} & \text{Maak de som} \\ &=a^2-\frac{95}{44}a+\frac{25}{22} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(\frac{-18}{6}+q)(b+\frac{18}{20})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{10}q-3b-3.\frac{9}{10}& \text{Uitwerken } \\ & =bq+\frac{9}{10}q-3b-\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{-6}{20})(\frac{-18}{11}-q)& =(\color{red}{x}+\color{orange}{\frac{3}{10}}).(\color{green}{-q}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{3}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{18}{11}x-\frac{3}{10}q-\frac{3}{10}.\frac{18}{11}& \text{Uitwerken } \\ & =-qx-\frac{18}{11}x-\frac{3}{10}q-\frac{54}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{18}{11}x-\frac{3}{10}q-\frac{27}{55} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-20}{10}+x)(q-\frac{-19}{11})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{11}x-2q-2.\frac{19}{11}& \text{Uitwerken } \\ & =qx+\frac{19}{11}x-2q-\frac{38}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-2}{14}+x)(\frac{8}{2}-b)& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{-b}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -bx+4x+\frac{1}{7}b-\frac{1}{7}.4& \text{Uitwerken } \\ & =-bx+4x+\frac{1}{7}b-\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{6}{3})(\frac{9}{15}+x)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{5}q-2x-2.\frac{3}{5}& \text{Uitwerken } \\ & =qx+\frac{3}{5}q-2x-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{4}{20}-x)(q-\frac{-6}{13})& =(\color{red}{-x}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{13}x+\frac{1}{5}q+\frac{1}{5}.\frac{6}{13}& \text{Uitwerken } \\ & =-qx-\frac{6}{13}x+\frac{1}{5}q+\frac{6}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-6}{11}-p)((-13)+b)& =(\color{red}{-p}+\color{orange}{\frac{-6}{11}}).(\color{green}{b}+\color{blue}{(-13)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-13)} + \color{orange}{(\frac{-6}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -bp+13p-\frac{6}{11}b+\frac{6}{11}.13& \text{Uitwerken } \\ & =-bp+13p-\frac{6}{11}b+\frac{78}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-14}{14})(\frac{12}{13}-q)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{12}{13}p+1q-1.\frac{12}{13}& \text{Uitwerken } \\ & =-pq+\frac{12}{13}p+1q-\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-17}{11}+q)(p-\frac{-14}{7})& =(\color{red}{q}+\color{orange}{\frac{-17}{11}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2q-\frac{17}{11}p-\frac{17}{11}.2& \text{Uitwerken } \\ & =pq+2q-\frac{17}{11}p-\frac{34}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)