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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-11}{17}+x)(\frac{-1}{8}+q)& =(\color{red}{x}+\color{orange}{\frac{-11}{17}}).(\color{green}{q}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{8}x-\frac{11}{17}q+\frac{11}{17}.\frac{1}{8}& \text{Uitwerken } \\ & =qx-\frac{1}{8}x-\frac{11}{17}q+\frac{11}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{7}{10})(\frac{-19}{13}+a)& =(\color{red}{x}+\color{orange}{\frac{-7}{10}}).(\color{green}{a}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{13}x-\frac{7}{10}a+\frac{7}{10}.\frac{19}{13}& \text{Uitwerken } \\ & =ax-\frac{19}{13}x-\frac{7}{10}a+\frac{133}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{-20}{17})(\frac{-5}{2}+p)& =(\color{red}{a}+\color{orange}{\frac{-20}{17}}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{2}a-\frac{20}{17}p+\frac{20}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =ap-\frac{5}{2}a-\frac{20}{17}p+\frac{100}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{5}{2}a-\frac{20}{17}p+\frac{50}{17} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a+\frac{18}{11})(a+\frac{-20}{17})& =(\color{red}{a}+\color{orange}{\frac{18}{11}}).(\color{green}{a}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{18}{11})} . \color{green}{(a)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{20}{17}a+\frac{18}{11}a-\frac{18}{11}.\frac{20}{17}& \text{Uitwerken } \\ & =a^2+((\frac{-20}{17})+\frac{18}{11})a-(\frac{-360}{187}) & \text{Neem samen} \\ &=a^2+\frac{86}{187}a-(\frac{-360}{187}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{15}{3}-p)(q+\frac{-8}{20})& =(\color{red}{-p}+\color{orange}{5}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(5)} . \color{green}{(q)} + \color{orange}{(5)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{5}p+5q-5.\frac{2}{5}& \text{Uitwerken } \\ & =-pq+\frac{2}{5}p+5q-\frac{10}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{2}{5}p+5q-2 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{5}{7})(a-\frac{-12}{20})& =(\color{red}{x}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{5}x-\frac{5}{7}a-\frac{5}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =ax+\frac{3}{5}x-\frac{5}{7}a-\frac{15}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{5}x-\frac{5}{7}a-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b+\frac{-12}{20})(a+\frac{-5}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{18})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-5}{18})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{18}b-\frac{3}{5}a+\frac{3}{5}.\frac{5}{18}& \text{Uitwerken } \\ & =ab-\frac{5}{18}b-\frac{3}{5}a+\frac{15}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{18}b-\frac{3}{5}a+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a+\frac{-11}{20})(a-\frac{17}{15})& =(\color{red}{a}+\color{orange}{\frac{-11}{20}}).(\color{green}{a}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{17}{15}a-\frac{11}{20}a+\frac{11}{20}.\frac{17}{15}& \text{Uitwerken } \\ & =a^2+((\frac{-17}{15})+(\frac{-11}{20}))a+\frac{187}{300} & \text{Neem samen} \\ &=a^2-\frac{101}{60}a+\frac{187}{300} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(q+\frac{-15}{13})(q-\frac{-19}{13})& =(\color{red}{q}+\color{orange}{\frac{-15}{13}}).(\color{green}{q}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{19}{13}q-\frac{15}{13}q-\frac{15}{13}.\frac{19}{13}& \text{Uitwerken } \\ & =q^2+(\frac{19}{13}+(\frac{-15}{13}))q-(\frac{-285}{169}) & \text{Neem samen} \\ &=q^2+\frac{4}{13}q-(\frac{-285}{169}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p-\frac{6}{4})(\frac{-13}{2}-a)& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{-a}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{2}p+\frac{3}{2}a+\frac{3}{2}.\frac{13}{2}& \text{Uitwerken } \\ & =-ap-\frac{13}{2}p+\frac{3}{2}a+\frac{39}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{1}{5}-x)(x-\frac{1}{7})& =(\color{red}{-x}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{7}x+\frac{1}{5}x-\frac{1}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{7}+\frac{1}{5})x-\frac{1}{35} & \text{Neem samen} \\ &=-x^2+\frac{12}{35}x-\frac{1}{35} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(b-\frac{9}{5})(a-\frac{-3}{8})& =(\color{red}{b}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{8}b-\frac{9}{5}a-\frac{9}{5}.\frac{3}{8}& \text{Uitwerken } \\ & =ab+\frac{3}{8}b-\frac{9}{5}a-\frac{27}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)