# Distributiviteit $$(a+r)(b+s)$$

#### Werk uit en vereenvoudig

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

#### Werk uit en vereenvoudig

##### Verbetersleutel

1. \begin{align}(a+\frac{-7}{6})(a-\frac{7}{15})& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{a}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{15}a-\frac{7}{6}a+\frac{7}{6}.\frac{7}{15}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{15})+(\frac{-7}{6}))a+\frac{49}{90} & \text{Neem samen} \\ &=a^2-\frac{49}{30}a+\frac{49}{90} & \text{Maak de som} \\\end{align}
2. \begin{align}(\frac{-9}{5}+a)(b-\frac{20}{10})& =(\color{red}{a}+\color{orange}{\frac{-9}{5}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2a-\frac{9}{5}b+\frac{9}{5}.2& \text{Uitwerken } \\ & =ab-2a-\frac{9}{5}b+\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
3. \begin{align}(\frac{10}{10}-b)((-19)+x)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{(-19)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-19)} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -bx+19b+1x-1.19& \text{Uitwerken } \\ & =-bx+19b+1x-19 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
4. \begin{align}(\frac{16}{19}-b)(\frac{-19}{4}-x)& =(\color{red}{-b}+\color{orange}{\frac{16}{19}}).(\color{green}{-x}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{16}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{4}b-\frac{16}{19}x-\frac{16}{19}.\frac{19}{4}& \text{Uitwerken } \\ & =bx+\frac{19}{4}b-\frac{16}{19}x-\frac{304}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{19}{4}b-\frac{16}{19}x-4 & \text{Vereenvoudig} \\\end{align}
5. \begin{align}(q-\frac{18}{17})(\frac{-6}{18}-p)& =(\color{red}{q}+\color{orange}{\frac{-18}{17}}).(\color{green}{-p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{3}q+\frac{18}{17}p+\frac{18}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =-pq-\frac{1}{3}q+\frac{18}{17}p+\frac{18}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{3}q+\frac{18}{17}p+\frac{6}{17} & \text{Vereenvoudig} \\\end{align}
6. \begin{align}(\frac{-7}{18}-b)(x-\frac{-5}{8})& =(\color{red}{-b}+\color{orange}{\frac{-7}{18}}).(\color{green}{x}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{8}b-\frac{7}{18}x-\frac{7}{18}.\frac{5}{8}& \text{Uitwerken } \\ & =-bx-\frac{5}{8}b-\frac{7}{18}x-\frac{35}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
7. \begin{align}(\frac{14}{5}+q)(a-\frac{-3}{8})& =(\color{red}{q}+\color{orange}{\frac{14}{5}}).(\color{green}{a}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{14}{5})} . \color{green}{(a)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{8}q+\frac{14}{5}a+\frac{14}{5}.\frac{3}{8}& \text{Uitwerken } \\ & =aq+\frac{3}{8}q+\frac{14}{5}a+\frac{42}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{8}q+\frac{14}{5}a+\frac{21}{20} & \text{Vereenvoudig} \\\end{align}
8. \begin{align}(\frac{-9}{12}+p)(\frac{-3}{19}-q)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-q}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{19}p+\frac{3}{4}q+\frac{3}{4}.\frac{3}{19}& \text{Uitwerken } \\ & =-pq-\frac{3}{19}p+\frac{3}{4}q+\frac{9}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
9. \begin{align}(x+\frac{-18}{10})(\frac{-5}{20}-p)& =(\color{red}{x}+\color{orange}{\frac{-9}{5}}).(\color{green}{-p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{4}x+\frac{9}{5}p+\frac{9}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =-px-\frac{1}{4}x+\frac{9}{5}p+\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
10. \begin{align}(\frac{18}{10}-q)(b+\frac{18}{20})& =(\color{red}{-q}+\color{orange}{\frac{9}{5}}).(\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}{(\frac{9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{10}q+\frac{9}{5}b+\frac{9}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =-bq-\frac{9}{10}q+\frac{9}{5}b+\frac{81}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
11. \begin{align}(\frac{20}{6}+x)(a-\frac{-7}{17})& =(\color{red}{x}+\color{orange}{\frac{10}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{17}x+\frac{10}{3}a+\frac{10}{3}.\frac{7}{17}& \text{Uitwerken } \\ & =ax+\frac{7}{17}x+\frac{10}{3}a+\frac{70}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
12. \begin{align}(\frac{12}{4}-a)(p-\frac{14}{7})& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(-2)} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ap+2a+3p-3.2& \text{Uitwerken } \\ & =-ap+2a+3p-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
Oefeningengenerator vanhoeckes.be/wiskunde 2024-08-09 05:44:58