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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{17}+p)(b-\frac{-14}{18})& =(\color{red}{p}+\color{orange}{\frac{-5}{17}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{9}p-\frac{5}{17}b-\frac{5}{17}.\frac{7}{9}& \text{Uitwerken } \\ & =bp+\frac{7}{9}p-\frac{5}{17}b-\frac{35}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p+\frac{-1}{14})(\frac{-7}{13}-p)& =(\color{red}{p}+\color{orange}{\frac{-1}{14}}).(\color{green}{-p}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{7}{13}p+\frac{1}{14}p+\frac{1}{14}.\frac{7}{13}& \text{Uitwerken } \\ & =-p^2+((\frac{-7}{13})+\frac{1}{14})p+(\frac{-7}{182}) & \text{Neem samen} \\ &=-p^2-\frac{85}{182}p+(\frac{-7}{182}) & \text{Maak de som} \\ &=-p^2-\frac{85}{182}p+(\frac{-1}{26}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{14}+x)(\frac{4}{7}-p)& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{-p}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{4}{7}x+\frac{1}{7}p-\frac{1}{7}.\frac{4}{7}& \text{Uitwerken } \\ & =-px+\frac{4}{7}x+\frac{1}{7}p-\frac{4}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{2}+a)(p-\frac{-1}{4})& =(\color{red}{a}+\color{orange}{8}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{4}a+8p+8.\frac{1}{4}& \text{Uitwerken } \\ & =ap+\frac{1}{4}a+8p+\frac{8}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{4}a+8p+2 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(q-\frac{-19}{14})(p-\frac{14}{16})& =(\color{red}{q}+\color{orange}{\frac{19}{14}}).(\color{green}{p}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{19}{14})} . \color{green}{(p)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{8}q+\frac{19}{14}p-\frac{19}{14}.\frac{7}{8}& \text{Uitwerken } \\ & =pq-\frac{7}{8}q+\frac{19}{14}p-\frac{133}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{8}q+\frac{19}{14}p-\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{5}{16}-p)(q+\frac{1}{14})& =(\color{red}{-p}+\color{orange}{\frac{5}{16}}).(\color{green}{q}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{5}{16})} . \color{green}{(q)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{14}p+\frac{5}{16}q+\frac{5}{16}.\frac{1}{14}& \text{Uitwerken } \\ & =-pq-\frac{1}{14}p+\frac{5}{16}q+\frac{5}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-10}{18}+b)(\frac{-16}{10}+q)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{5}b-\frac{5}{9}q+\frac{5}{9}.\frac{8}{5}& \text{Uitwerken } \\ & =bq-\frac{8}{5}b-\frac{5}{9}q+\frac{40}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{8}{5}b-\frac{5}{9}q+\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{6}{5}-x)(p+\frac{-9}{17})& =(\color{red}{-x}+\color{orange}{\frac{6}{5}}).(\color{green}{p}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{17}x+\frac{6}{5}p-\frac{6}{5}.\frac{9}{17}& \text{Uitwerken } \\ & =-px+\frac{9}{17}x+\frac{6}{5}p-\frac{54}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-15}{16}-x)(q-\frac{9}{9})& =(\color{red}{-x}+\color{orange}{\frac{-15}{16}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x-\frac{15}{16}q+\frac{15}{16}.1& \text{Uitwerken } \\ & =-qx+1x-\frac{15}{16}q+\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{4}{11}+p)(\frac{7}{13}+x)& =(\color{red}{p}+\color{orange}{\frac{4}{11}}).(\color{green}{x}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{13}p+\frac{4}{11}x+\frac{4}{11}.\frac{7}{13}& \text{Uitwerken } \\ & =px+\frac{7}{13}p+\frac{4}{11}x+\frac{28}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-5}{15})((-4)-x)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{-x}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -px-4p+\frac{1}{3}x+\frac{1}{3}.4& \text{Uitwerken } \\ & =-px-4p+\frac{1}{3}x+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{8}{2})(\frac{-4}{20}-x)& =(\color{red}{p}+\color{orange}{4}).(\color{green}{-x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(4)} . \color{green}{(-x)} + \color{orange}{(4)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{5}p-4x-4.\frac{1}{5}& \text{Uitwerken } \\ & =-px-\frac{1}{5}p-4x-\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)