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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-16}{11}-p)(b+\frac{-5}{11})& =(\color{red}{-p}+\color{orange}{\frac{-16}{11}}).(\color{green}{b}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{11}p-\frac{16}{11}b+\frac{16}{11}.\frac{5}{11}& \text{Uitwerken } \\ & =-bp+\frac{5}{11}p-\frac{16}{11}b+\frac{80}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{1}{11}+q)(\frac{-11}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{11}}).(\color{green}{a}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{1}{11})} . \color{green}{(a)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{20}q+\frac{1}{11}a-\frac{1}{11}.\frac{11}{20}& \text{Uitwerken } \\ & =aq-\frac{11}{20}q+\frac{1}{11}a-\frac{11}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{11}{20}q+\frac{1}{11}a-\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{6}+x)(a+\frac{16}{11})& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{11}x-\frac{1}{6}a-\frac{1}{6}.\frac{16}{11}& \text{Uitwerken } \\ & =ax+\frac{16}{11}x-\frac{1}{6}a-\frac{16}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{16}{11}x-\frac{1}{6}a-\frac{8}{33} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{17}{12}+q)(\frac{-16}{19}+x)& =(\color{red}{q}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{19}q+\frac{17}{12}x-\frac{17}{12}.\frac{16}{19}& \text{Uitwerken } \\ & =qx-\frac{16}{19}q+\frac{17}{12}x-\frac{272}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{16}{19}q+\frac{17}{12}x-\frac{68}{57} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{-9}{12})(q+\frac{-11}{6})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{6}x-\frac{3}{4}q+\frac{3}{4}.\frac{11}{6}& \text{Uitwerken } \\ & =qx-\frac{11}{6}x-\frac{3}{4}q+\frac{33}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{11}{6}x-\frac{3}{4}q+\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{3}{17}+b)(\frac{11}{14}-b)& =(\color{red}{b}+\color{orange}{\frac{3}{17}}).(\color{green}{-b}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{3}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{11}{14}b-\frac{3}{17}b+\frac{3}{17}.\frac{11}{14}& \text{Uitwerken } \\ & =-b^2+(\frac{11}{14}+(\frac{-3}{17}))b+(\frac{-33}{238}) & \text{Neem samen} \\ &=-b^2+\frac{145}{238}b+(\frac{-33}{238}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-7}{14}+a)(\frac{10}{15}-b)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{3}a+\frac{1}{2}b-\frac{1}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab+\frac{2}{3}a+\frac{1}{2}b-\frac{2}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{2}{3}a+\frac{1}{2}b-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{-18}{6})(\frac{-9}{11}+b)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{11})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-9}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{11}q+3b-3.\frac{9}{11}& \text{Uitwerken } \\ & =bq-\frac{9}{11}q+3b-\frac{27}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-17}{8}-x)(p-\frac{-8}{19})& =(\color{red}{-x}+\color{orange}{\frac{-17}{8}}).(\color{green}{p}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{8}{19}x-\frac{17}{8}p-\frac{17}{8}.\frac{8}{19}& \text{Uitwerken } \\ & =-px-\frac{8}{19}x-\frac{17}{8}p-\frac{136}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{8}{19}x-\frac{17}{8}p-\frac{17}{19} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{19}{11}+a)(p-\frac{17}{8})& =(\color{red}{a}+\color{orange}{\frac{19}{11}}).(\color{green}{p}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(\frac{19}{11})} . \color{green}{(p)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{8}a+\frac{19}{11}p-\frac{19}{11}.\frac{17}{8}& \text{Uitwerken } \\ & =ap-\frac{17}{8}a+\frac{19}{11}p-\frac{323}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{20}{14})(x-\frac{8}{5})& =(\color{red}{a}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{5}a-\frac{10}{7}x+\frac{10}{7}.\frac{8}{5}& \text{Uitwerken } \\ & =ax-\frac{8}{5}a-\frac{10}{7}x+\frac{80}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{8}{5}a-\frac{10}{7}x+\frac{16}{7} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x-\frac{12}{20})(\frac{-17}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{16}x-\frac{3}{5}a+\frac{3}{5}.\frac{17}{16}& \text{Uitwerken } \\ & =ax-\frac{17}{16}x-\frac{3}{5}a+\frac{51}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)