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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{1}{14})(p+\frac{13}{4})& =(\color{red}{a}+\color{orange}{\frac{-1}{14}}).(\color{green}{p}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{4}a-\frac{1}{14}p-\frac{1}{14}.\frac{13}{4}& \text{Uitwerken } \\ & =ap+\frac{13}{4}a-\frac{1}{14}p-\frac{13}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{-8}{20})(b+\frac{-9}{20})& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{20}a+\frac{2}{5}b-\frac{2}{5}.\frac{9}{20}& \text{Uitwerken } \\ & =ab-\frac{9}{20}a+\frac{2}{5}b-\frac{18}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{20}a+\frac{2}{5}b-\frac{9}{50} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-4}{18}-q)(b-\frac{-20}{11})& =(\color{red}{-q}+\color{orange}{\frac{-2}{9}}).(\color{green}{b}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{20}{11}q-\frac{2}{9}b-\frac{2}{9}.\frac{20}{11}& \text{Uitwerken } \\ & =-bq-\frac{20}{11}q-\frac{2}{9}b-\frac{40}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{5}{16})(\frac{-5}{15}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{16}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}x-\frac{5}{16}a+\frac{5}{16}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}x-\frac{5}{16}a+\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{17}{18}+a)(b-\frac{-19}{11})& =(\color{red}{a}+\color{orange}{\frac{17}{18}}).(\color{green}{b}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{17}{18})} . \color{green}{(b)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{11}a+\frac{17}{18}b+\frac{17}{18}.\frac{19}{11}& \text{Uitwerken } \\ & =ab+\frac{19}{11}a+\frac{17}{18}b+\frac{323}{198} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-20}{19}-p)(\frac{-12}{3}-q)& =(\color{red}{-p}+\color{orange}{\frac{-20}{19}}).(\color{green}{-q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-20}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pq+4p+\frac{20}{19}q+\frac{20}{19}.4& \text{Uitwerken } \\ & =pq+4p+\frac{20}{19}q+\frac{80}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-10}{13}+x)(\frac{17}{13}-q)& =(\color{red}{x}+\color{orange}{\frac{-10}{13}}).(\color{green}{-q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{13}x+\frac{10}{13}q-\frac{10}{13}.\frac{17}{13}& \text{Uitwerken } \\ & =-qx+\frac{17}{13}x+\frac{10}{13}q-\frac{170}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{18}{5}-b)(\frac{2}{14}+x)& =(\color{red}{-b}+\color{orange}{\frac{18}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{18}{5})} . \color{green}{(x)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{7}b+\frac{18}{5}x+\frac{18}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =-bx-\frac{1}{7}b+\frac{18}{5}x+\frac{18}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{8}{3}-b)(x+\frac{4}{6})& =(\color{red}{-b}+\color{orange}{\frac{8}{3}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{3}b+\frac{8}{3}x+\frac{8}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-bx-\frac{2}{3}b+\frac{8}{3}x+\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{4}{20}+x)(a-\frac{2}{15})& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{15}x+\frac{1}{5}a-\frac{1}{5}.\frac{2}{15}& \text{Uitwerken } \\ & =ax-\frac{2}{15}x+\frac{1}{5}a-\frac{2}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{20}{5})(\frac{-19}{20}+b)& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{20}a-4b+4.\frac{19}{20}& \text{Uitwerken } \\ & =ab-\frac{19}{20}a-4b+\frac{76}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{19}{20}a-4b+\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-19}{2}-a)(\frac{11}{6}+p)& =(\color{red}{-a}+\color{orange}{\frac{-19}{2}}).(\color{green}{p}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{6}a-\frac{19}{2}p-\frac{19}{2}.\frac{11}{6}& \text{Uitwerken } \\ & =-ap-\frac{11}{6}a-\frac{19}{2}p-\frac{209}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)