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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-11}{20})(p+\frac{-3}{17})& =(\color{red}{b}+\color{orange}{\frac{-11}{20}}).(\color{green}{p}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{17}b-\frac{11}{20}p+\frac{11}{20}.\frac{3}{17}& \text{Uitwerken } \\ & =bp-\frac{3}{17}b-\frac{11}{20}p+\frac{33}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-14}{14}-a)(\frac{-9}{6}+p)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{2}a-1p+1.\frac{3}{2}& \text{Uitwerken } \\ & =-ap+\frac{3}{2}a-1p+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{14}{13}-q)(b-\frac{15}{11})& =(\color{red}{-q}+\color{orange}{\frac{14}{13}}).(\color{green}{b}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{14}{13})} . \color{green}{(b)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{15}{11}q+\frac{14}{13}b-\frac{14}{13}.\frac{15}{11}& \text{Uitwerken } \\ & =-bq+\frac{15}{11}q+\frac{14}{13}b-\frac{210}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{9}{7}+q)(b+\frac{20}{9})& =(\color{red}{q}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{20}{9}q+\frac{9}{7}b+\frac{9}{7}.\frac{20}{9}& \text{Uitwerken } \\ & =bq+\frac{20}{9}q+\frac{9}{7}b+\frac{180}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{20}{9}q+\frac{9}{7}b+\frac{20}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b-\frac{11}{17})(b-\frac{-3}{11})& =(\color{red}{b}+\color{orange}{\frac{-11}{17}}).(\color{green}{b}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{11}b-\frac{11}{17}b-\frac{11}{17}.\frac{3}{11}& \text{Uitwerken } \\ & =b^2+(\frac{3}{11}+(\frac{-11}{17}))b-(\frac{-33}{187}) & \text{Neem samen} \\ &=b^2-\frac{70}{187}b-(\frac{-33}{187}) & \text{Maak de som} \\ &=b^2-\frac{70}{187}b+\frac{3}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
6. \(\begin{align}(\frac{7}{17}-p)(\frac{-16}{11}-p)& =(\color{red}{-p}+\color{orange}{\frac{7}{17}}).(\color{green}{-p}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{7}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{16}{11}p-\frac{7}{17}p-\frac{7}{17}.\frac{16}{11}& \text{Uitwerken } \\ & =p^2+(\frac{16}{11}+(\frac{-7}{17}))p-(\frac{-112}{187}) & \text{Neem samen} \\ &=p^2+\frac{195}{187}p-(\frac{-112}{187}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{10}{16}+q)(\frac{17}{10}+x)& =(\color{red}{q}+\color{orange}{\frac{5}{8}}).(\color{green}{x}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{10}q+\frac{5}{8}x+\frac{5}{8}.\frac{17}{10}& \text{Uitwerken } \\ & =qx+\frac{17}{10}q+\frac{5}{8}x+\frac{85}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{17}{10}q+\frac{5}{8}x+\frac{17}{16} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x+\frac{8}{20})(b-\frac{9}{3})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx-3x+\frac{2}{5}b-\frac{2}{5}.3& \text{Uitwerken } \\ & =bx-3x+\frac{2}{5}b-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{-10}{18})(b+\frac{-12}{14})& =(\color{red}{a}+\color{orange}{\frac{5}{9}}).(\color{green}{b}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{7}a+\frac{5}{9}b-\frac{5}{9}.\frac{6}{7}& \text{Uitwerken } \\ & =ab-\frac{6}{7}a+\frac{5}{9}b-\frac{30}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{7}a+\frac{5}{9}b-\frac{10}{21} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{20}{10})(p+\frac{3}{8})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{8}a-2p-2.\frac{3}{8}& \text{Uitwerken } \\ & =ap+\frac{3}{8}a-2p-\frac{6}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{8}a-2p-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{3}{6}+p)(p+(-2))& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p+\frac{1}{2}p-\frac{1}{2}.2& \text{Uitwerken } \\ & =p^2+((-2)+\frac{1}{2})p-(\frac{-2}{2}) & \text{Neem samen} \\ &=p^2-\frac{3}{2}p-(\frac{-2}{2}) & \text{Maak de som} \\ &=p^2-\frac{3}{2}p+1 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
12. \(\begin{align}(\frac{11}{17}+p)(\frac{-19}{2}-p)& =(\color{red}{p}+\color{orange}{\frac{11}{17}}).(\color{green}{-p}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{11}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{2}p-\frac{11}{17}p-\frac{11}{17}.\frac{19}{2}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{2})+(\frac{-11}{17}))p-\frac{209}{34} & \text{Neem samen} \\ &=-p^2-\frac{345}{34}p-\frac{209}{34} & \text{Maak de som} \\\end{align}\)