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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-12}{5}+x)(p-\frac{-11}{19})& =(\color{red}{x}+\color{orange}{\frac{-12}{5}}).(\color{green}{p}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{19}x-\frac{12}{5}p-\frac{12}{5}.\frac{11}{19}& \text{Uitwerken } \\ & =px+\frac{11}{19}x-\frac{12}{5}p-\frac{132}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{-14}{5})(b-\frac{-1}{3})& =(\color{red}{q}+\color{orange}{\frac{14}{5}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{14}{5})} . \color{green}{(b)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}q+\frac{14}{5}b+\frac{14}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}q+\frac{14}{5}b+\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-3}{20}+b)(a-\frac{5}{15})& =(\color{red}{b}+\color{orange}{\frac{-3}{20}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{3}b-\frac{3}{20}a+\frac{3}{20}.\frac{1}{3}& \text{Uitwerken } \\ & =ab-\frac{1}{3}b-\frac{3}{20}a+\frac{3}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{3}b-\frac{3}{20}a+\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-7}{12}+p)(a-\frac{-2}{3})& =(\color{red}{p}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{3}p-\frac{7}{12}a-\frac{7}{12}.\frac{2}{3}& \text{Uitwerken } \\ & =ap+\frac{2}{3}p-\frac{7}{12}a-\frac{14}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{2}{3}p-\frac{7}{12}a-\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a+\frac{20}{6})(\frac{7}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{6}a+\frac{10}{3}p+\frac{10}{3}.\frac{7}{6}& \text{Uitwerken } \\ & =ap+\frac{7}{6}a+\frac{10}{3}p+\frac{70}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{7}{6}a+\frac{10}{3}p+\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q-\frac{-12}{19})(p+\frac{7}{20})& =(\color{red}{q}+\color{orange}{\frac{12}{19}}).(\color{green}{p}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{12}{19})} . \color{green}{(p)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{20}q+\frac{12}{19}p+\frac{12}{19}.\frac{7}{20}& \text{Uitwerken } \\ & =pq+\frac{7}{20}q+\frac{12}{19}p+\frac{84}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{7}{20}q+\frac{12}{19}p+\frac{21}{95} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{4}{9}+x)(\frac{-4}{6}-q)& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{-q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{3}x-\frac{4}{9}q-\frac{4}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =-qx-\frac{2}{3}x-\frac{4}{9}q-\frac{8}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{-16}{14})(\frac{-19}{4}-p)& =(\color{red}{x}+\color{orange}{\frac{-8}{7}}).(\color{green}{-p}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{4}x+\frac{8}{7}p+\frac{8}{7}.\frac{19}{4}& \text{Uitwerken } \\ & =-px-\frac{19}{4}x+\frac{8}{7}p+\frac{152}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{19}{4}x+\frac{8}{7}p+\frac{38}{7} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-(-17))(\frac{-19}{15}-p)& =(\color{red}{x}+\color{orange}{17}).(\color{green}{-p}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(17)} . \color{green}{(-p)} + \color{orange}{(17)} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{15}x-17p-17.\frac{19}{15}& \text{Uitwerken } \\ & =-px-\frac{19}{15}x-17p-\frac{323}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{-12}{2})(\frac{-17}{13}-p)& =(\color{red}{b}+\color{orange}{6}).(\color{green}{-p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(6)} . \color{green}{(-p)} + \color{orange}{(6)} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{17}{13}b-6p-6.\frac{17}{13}& \text{Uitwerken } \\ & =-bp-\frac{17}{13}b-6p-\frac{102}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q+\frac{1}{14})((-19)+q)& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{q}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-19)} + \color{orange}{(\frac{1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = qq-19q+\frac{1}{14}q-\frac{1}{14}.19& \text{Uitwerken } \\ & =q^2+((-19)+\frac{1}{14})q-(\frac{-19}{14}) & \text{Neem samen} \\ &=q^2-\frac{265}{14}q-(\frac{-19}{14}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p-\frac{-13}{4})(a+\frac{12}{19})& =(\color{red}{p}+\color{orange}{\frac{13}{4}}).(\color{green}{a}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{12}{19}p+\frac{13}{4}a+\frac{13}{4}.\frac{12}{19}& \text{Uitwerken } \\ & =ap+\frac{12}{19}p+\frac{13}{4}a+\frac{156}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{12}{19}p+\frac{13}{4}a+\frac{39}{19} & \text{Vereenvoudig} \\\end{align}\)