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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-1}{4})(p-\frac{2}{16})& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{8}p-\frac{1}{4}p+\frac{1}{4}.\frac{1}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{8})+(\frac{-1}{4}))p+\frac{1}{32} & \text{Neem samen} \\ &=p^2-\frac{3}{8}p+\frac{1}{32} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-5}{5}-x)(x-\frac{-8}{2})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(4)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -xx-4x-1x-1.4& \text{Uitwerken } \\ & =-x^2+((-4)+(-1))x-4 & \text{Neem samen} \\ &=-x^2-5x-4 & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{17}{4}+a)(\frac{15}{12}+x)& =(\color{red}{a}+\color{orange}{\frac{17}{4}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{17}{4})} . \color{green}{(x)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{4}a+\frac{17}{4}x+\frac{17}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =ax+\frac{5}{4}a+\frac{17}{4}x+\frac{85}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{20}{3})(\frac{-4}{19}-q)& =(\color{red}{b}+\color{orange}{\frac{-20}{3}}).(\color{green}{-q}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{19}b+\frac{20}{3}q+\frac{20}{3}.\frac{4}{19}& \text{Uitwerken } \\ & =-bq-\frac{4}{19}b+\frac{20}{3}q+\frac{80}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-19}{9}-q)(\frac{-12}{13}-x)& =(\color{red}{-q}+\color{orange}{\frac{-19}{9}}).(\color{green}{-x}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{13}q+\frac{19}{9}x+\frac{19}{9}.\frac{12}{13}& \text{Uitwerken } \\ & =qx+\frac{12}{13}q+\frac{19}{9}x+\frac{228}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{13}q+\frac{19}{9}x+\frac{76}{39} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{16}{17}-p)(\frac{-20}{10}-a)& =(\color{red}{-p}+\color{orange}{\frac{16}{17}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{16}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap+2p-\frac{16}{17}a-\frac{16}{17}.2& \text{Uitwerken } \\ & =ap+2p-\frac{16}{17}a-\frac{32}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{6}{18})(\frac{-13}{6}+q)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{6}x+\frac{1}{3}q-\frac{1}{3}.\frac{13}{6}& \text{Uitwerken } \\ & =qx-\frac{13}{6}x+\frac{1}{3}q-\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-9}{7}-b)(b-\frac{8}{4})& =(\color{red}{-b}+\color{orange}{\frac{-9}{7}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bb+2b-\frac{9}{7}b+\frac{9}{7}.2& \text{Uitwerken } \\ & =-b^2+(2+(\frac{-9}{7}))b+(\frac{-18}{7}) & \text{Neem samen} \\ &=-b^2+\frac{5}{7}b+(\frac{-18}{7}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(a-\frac{-5}{11})(\frac{-4}{8}+a)& =(\color{red}{a}+\color{orange}{\frac{5}{11}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{11})} . \color{green}{(a)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{2}a+\frac{5}{11}a-\frac{5}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{2})+\frac{5}{11})a-(\frac{-5}{22}) & \text{Neem samen} \\ &=a^2-\frac{1}{22}a-(\frac{-5}{22}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{17}{15}+p)(\frac{-11}{15}-q)& =(\color{red}{p}+\color{orange}{\frac{17}{15}}).(\color{green}{-q}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{17}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{15}p-\frac{17}{15}q-\frac{17}{15}.\frac{11}{15}& \text{Uitwerken } \\ & =-pq-\frac{11}{15}p-\frac{17}{15}q-\frac{187}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{-7}{14})(b+\frac{17}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{15}x-\frac{1}{2}b-\frac{1}{2}.\frac{17}{15}& \text{Uitwerken } \\ & =bx+\frac{17}{15}x-\frac{1}{2}b-\frac{17}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-5}{4})(5-b)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{-b}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -bp+5p+\frac{5}{4}b-\frac{5}{4}.5& \text{Uitwerken } \\ & =-bp+5p+\frac{5}{4}b-\frac{25}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)