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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-14}{9})(\frac{4}{8}-x)& =(\color{red}{p}+\color{orange}{\frac{14}{9}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{14}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{2}p-\frac{14}{9}x+\frac{14}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =-px+\frac{1}{2}p-\frac{14}{9}x+\frac{14}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{1}{2}p-\frac{14}{9}x+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(q+\frac{20}{10})(\frac{20}{17}-p)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{20}{17}q-2p+2.\frac{20}{17}& \text{Uitwerken } \\ & =-pq+\frac{20}{17}q-2p+\frac{40}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{18}{9})(\frac{12}{7}-x)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{12}{7}x-2x+2.\frac{12}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{12}{7}+(-2))x+(\frac{-24}{7}) & \text{Neem samen} \\ &=-x^2-\frac{2}{7}x+(\frac{-24}{7}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(a+\frac{-10}{4})(b-(-13))& =(\color{red}{a}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{13})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(13)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = ab+13a-\frac{5}{2}b-\frac{5}{2}.13& \text{Uitwerken } \\ & =ab+13a-\frac{5}{2}b-\frac{65}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-1}{3})(b+\frac{8}{13})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{13}p-\frac{1}{3}b-\frac{1}{3}.\frac{8}{13}& \text{Uitwerken } \\ & =bp+\frac{8}{13}p-\frac{1}{3}b-\frac{8}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{17}{12}+x)(\frac{-12}{8}-b)& =(\color{red}{x}+\color{orange}{\frac{17}{12}}).(\color{green}{-b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{17}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{2}x-\frac{17}{12}b-\frac{17}{12}.\frac{3}{2}& \text{Uitwerken } \\ & =-bx-\frac{3}{2}x-\frac{17}{12}b-\frac{51}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{3}{2}x-\frac{17}{12}b-\frac{17}{8} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+\frac{-17}{3})(b+\frac{5}{8})& =(\color{red}{q}+\color{orange}{\frac{-17}{3}}).(\color{green}{b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{8}q-\frac{17}{3}b-\frac{17}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =bq+\frac{5}{8}q-\frac{17}{3}b-\frac{85}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{8}{7})(a+\frac{9}{10})& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{10}q-\frac{8}{7}a-\frac{8}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =aq+\frac{9}{10}q-\frac{8}{7}a-\frac{72}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{9}{10}q-\frac{8}{7}a-\frac{36}{35} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(b+\frac{-12}{9})(q+\frac{-19}{15})& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{15}b-\frac{4}{3}q+\frac{4}{3}.\frac{19}{15}& \text{Uitwerken } \\ & =bq-\frac{19}{15}b-\frac{4}{3}q+\frac{76}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{-17}{13})(\frac{-15}{9}-q)& =(\color{red}{p}+\color{orange}{\frac{17}{13}}).(\color{green}{-q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{17}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{3}p-\frac{17}{13}q-\frac{17}{13}.\frac{5}{3}& \text{Uitwerken } \\ & =-pq-\frac{5}{3}p-\frac{17}{13}q-\frac{85}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{-7}{12})(\frac{10}{8}-p)& =(\color{red}{q}+\color{orange}{\frac{7}{12}}).(\color{green}{-p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{7}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{4}q-\frac{7}{12}p+\frac{7}{12}.\frac{5}{4}& \text{Uitwerken } \\ & =-pq+\frac{5}{4}q-\frac{7}{12}p+\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{4}{13})(a+\frac{20}{10})& =(\color{red}{p}+\color{orange}{\frac{4}{13}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{4}{13})} . \color{green}{(a)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2p+\frac{4}{13}a+\frac{4}{13}.2& \text{Uitwerken } \\ & =ap+2p+\frac{4}{13}a+\frac{8}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)