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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{-13}{16})(\frac{-4}{7}-p)& =(\color{red}{q}+\color{orange}{\frac{-13}{16}}).(\color{green}{-p}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{7}q+\frac{13}{16}p+\frac{13}{16}.\frac{4}{7}& \text{Uitwerken } \\ & =-pq-\frac{4}{7}q+\frac{13}{16}p+\frac{52}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{4}{7}q+\frac{13}{16}p+\frac{13}{28} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b+\frac{-5}{14})(x+\frac{-12}{18})& =(\color{red}{b}+\color{orange}{\frac{-5}{14}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{3}b-\frac{5}{14}x+\frac{5}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =bx-\frac{2}{3}b-\frac{5}{14}x+\frac{10}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{2}{3}b-\frac{5}{14}x+\frac{5}{21} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{15}{4}+x)(\frac{16}{17}+p)& =(\color{red}{x}+\color{orange}{\frac{15}{4}}).(\color{green}{p}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{15}{4})} . \color{green}{(p)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{16}{17}x+\frac{15}{4}p+\frac{15}{4}.\frac{16}{17}& \text{Uitwerken } \\ & =px+\frac{16}{17}x+\frac{15}{4}p+\frac{240}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{16}{17}x+\frac{15}{4}p+\frac{60}{17} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a-\frac{-4}{5})(x-\frac{17}{12})& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{12}a+\frac{4}{5}x-\frac{4}{5}.\frac{17}{12}& \text{Uitwerken } \\ & =ax-\frac{17}{12}a+\frac{4}{5}x-\frac{68}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{12}a+\frac{4}{5}x-\frac{17}{15} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b+\frac{12}{9})(x-\frac{18}{13})& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{13}b+\frac{4}{3}x-\frac{4}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =bx-\frac{18}{13}b+\frac{4}{3}x-\frac{72}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{18}{13}b+\frac{4}{3}x-\frac{24}{13} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q+\frac{4}{13})(\frac{-6}{10}-b)& =(\color{red}{q}+\color{orange}{\frac{4}{13}}).(\color{green}{-b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{4}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{5}q-\frac{4}{13}b-\frac{4}{13}.\frac{3}{5}& \text{Uitwerken } \\ & =-bq-\frac{3}{5}q-\frac{4}{13}b-\frac{12}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-8)(\frac{11}{13}-b)& =(\color{red}{a}+\color{orange}{(-8)}).(\color{green}{-b}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(-8)} . \color{green}{(-b)} + \color{orange}{(-8)} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{13}a+8b-8.\frac{11}{13}& \text{Uitwerken } \\ & =-ab+\frac{11}{13}a+8b-\frac{88}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{9}{11})(\frac{11}{5}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{11}}).(\color{green}{b}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{5}b-\frac{9}{11}b-\frac{9}{11}.\frac{11}{5}& \text{Uitwerken } \\ & =b^2+(\frac{11}{5}+(\frac{-9}{11}))b-(\frac{-99}{55}) & \text{Neem samen} \\ &=b^2+\frac{76}{55}b-(\frac{-99}{55}) & \text{Maak de som} \\ &=b^2+\frac{76}{55}b+\frac{9}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(a-\frac{19}{4})(\frac{20}{13}+p)& =(\color{red}{a}+\color{orange}{\frac{-19}{4}}).(\color{green}{p}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{13}a-\frac{19}{4}p-\frac{19}{4}.\frac{20}{13}& \text{Uitwerken } \\ & =ap+\frac{20}{13}a-\frac{19}{4}p-\frac{380}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{13}a-\frac{19}{4}p-\frac{95}{13} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-9}{12}-a)(\frac{20}{17}-p)& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-p}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{20}{17}a+\frac{3}{4}p-\frac{3}{4}.\frac{20}{17}& \text{Uitwerken } \\ & =ap-\frac{20}{17}a+\frac{3}{4}p-\frac{60}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{20}{17}a+\frac{3}{4}p-\frac{15}{17} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-\frac{11}{8})(\frac{-7}{20}+a)& =(\color{red}{b}+\color{orange}{\frac{-11}{8}}).(\color{green}{a}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{20}b-\frac{11}{8}a+\frac{11}{8}.\frac{7}{20}& \text{Uitwerken } \\ & =ab-\frac{7}{20}b-\frac{11}{8}a+\frac{77}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{11}{16})(b-\frac{18}{4})& =(\color{red}{x}+\color{orange}{\frac{-11}{16}}).(\color{green}{b}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{2}x-\frac{11}{16}b+\frac{11}{16}.\frac{9}{2}& \text{Uitwerken } \\ & =bx-\frac{9}{2}x-\frac{11}{16}b+\frac{99}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)