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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{5}-b)(\frac{-4}{18}+q)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{9}b-1q+1.\frac{2}{9}& \text{Uitwerken } \\ & =-bq+\frac{2}{9}b-1q+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{-19}{2})(\frac{-8}{2}+b)& =(\color{red}{q}+\color{orange}{\frac{-19}{2}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-19}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bq-4q-\frac{19}{2}b+\frac{19}{2}.4& \text{Uitwerken } \\ & =bq-4q-\frac{19}{2}b+\frac{76}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-4q-\frac{19}{2}b+38 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a+\frac{18}{5})(x+\frac{3}{17})& =(\color{red}{a}+\color{orange}{\frac{18}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{18}{5})} . \color{green}{(x)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{17}a+\frac{18}{5}x+\frac{18}{5}.\frac{3}{17}& \text{Uitwerken } \\ & =ax+\frac{3}{17}a+\frac{18}{5}x+\frac{54}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b+\frac{1}{9})(a-\frac{3}{18})& =(\color{red}{b}+\color{orange}{\frac{1}{9}}).(\color{green}{a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{6}b+\frac{1}{9}a-\frac{1}{9}.\frac{1}{6}& \text{Uitwerken } \\ & =ab-\frac{1}{6}b+\frac{1}{9}a-\frac{1}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{3}{20}-x)(a+\frac{9}{16})& =(\color{red}{-x}+\color{orange}{\frac{3}{20}}).(\color{green}{a}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{3}{20})} . \color{green}{(a)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{16}x+\frac{3}{20}a+\frac{3}{20}.\frac{9}{16}& \text{Uitwerken } \\ & =-ax-\frac{9}{16}x+\frac{3}{20}a+\frac{27}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{8}{3}-x)(\frac{-10}{20}-p)& =(\color{red}{-x}+\color{orange}{\frac{8}{3}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{2}x-\frac{8}{3}p-\frac{8}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =px+\frac{1}{2}x-\frac{8}{3}p-\frac{8}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{2}x-\frac{8}{3}p-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{17}{2}+b)(\frac{9}{16}+p)& =(\color{red}{b}+\color{orange}{\frac{17}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{17}{2})} . \color{green}{(p)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{16}b+\frac{17}{2}p+\frac{17}{2}.\frac{9}{16}& \text{Uitwerken } \\ & =bp+\frac{9}{16}b+\frac{17}{2}p+\frac{153}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{13}{8}+a)(p-\frac{-4}{16})& =(\color{red}{a}+\color{orange}{\frac{13}{8}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{13}{8})} . \color{green}{(p)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{4}a+\frac{13}{8}p+\frac{13}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =ap+\frac{1}{4}a+\frac{13}{8}p+\frac{13}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{4}{12})(x+\frac{-19}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{10}x+\frac{1}{3}x-\frac{1}{3}.\frac{19}{10}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{10})+\frac{1}{3})x-(\frac{-19}{30}) & \text{Neem samen} \\ &=x^2-\frac{47}{30}x-(\frac{-19}{30}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}((-14)-a)(\frac{15}{19}-q)& =(\color{red}{-a}+\color{orange}{(-14)}).(\color{green}{-q}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(-14)} . \color{green}{(-q)} + \color{orange}{(-14)} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{19}a+14q-14.\frac{15}{19}& \text{Uitwerken } \\ & =aq-\frac{15}{19}a+14q-\frac{210}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{1}{5}-a)(a-\frac{-17}{17})& =(\color{red}{-a}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aa-1a+\frac{1}{5}a+\frac{1}{5}.1& \text{Uitwerken } \\ & =-a^2+((-1)+\frac{1}{5})a+(\frac{-1}{5}) & \text{Neem samen} \\ &=-a^2-\frac{4}{5}a+(\frac{-1}{5}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q+\frac{-11}{3})(\frac{-15}{6}-x)& =(\color{red}{q}+\color{orange}{\frac{-11}{3}}).(\color{green}{-x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{2}q+\frac{11}{3}x+\frac{11}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-qx-\frac{5}{2}q+\frac{11}{3}x+\frac{55}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)