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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-4}{19})(\frac{16}{18}+q)& =(\color{red}{b}+\color{orange}{\frac{4}{19}}).(\color{green}{q}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{4}{19})} . \color{green}{(q)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{9}b+\frac{4}{19}q+\frac{4}{19}.\frac{8}{9}& \text{Uitwerken } \\ & =bq+\frac{8}{9}b+\frac{4}{19}q+\frac{32}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-20}{9})(x+\frac{17}{18})& =(\color{red}{p}+\color{orange}{\frac{20}{9}}).(\color{green}{x}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{20}{9})} . \color{green}{(x)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{18}p+\frac{20}{9}x+\frac{20}{9}.\frac{17}{18}& \text{Uitwerken } \\ & =px+\frac{17}{18}p+\frac{20}{9}x+\frac{340}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{17}{18}p+\frac{20}{9}x+\frac{170}{81} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{3}{9}-a)(\frac{-4}{20}-b)& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{5}a-\frac{1}{3}b-\frac{1}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =ab+\frac{1}{5}a-\frac{1}{3}b-\frac{1}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{-19}{14})(q-\frac{-10}{16})& =(\color{red}{x}+\color{orange}{\frac{19}{14}}).(\color{green}{q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{19}{14})} . \color{green}{(q)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{8}x+\frac{19}{14}q+\frac{19}{14}.\frac{5}{8}& \text{Uitwerken } \\ & =qx+\frac{5}{8}x+\frac{19}{14}q+\frac{95}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{7}{20})(\frac{1}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{7}{20}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}b+\frac{7}{20}a+\frac{7}{20}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}b+\frac{7}{20}a+\frac{7}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-10}{4}-x)(x-\frac{-2}{2})& =(\color{red}{-x}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -xx-1x-\frac{5}{2}x-\frac{5}{2}.1& \text{Uitwerken } \\ & =-x^2+((-1)+(\frac{-5}{2}))x-\frac{5}{2} & \text{Neem samen} \\ &=-x^2-\frac{7}{2}x-\frac{5}{2} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(p+\frac{-14}{6})(\frac{-17}{5}+x)& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{x}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{5}p-\frac{7}{3}x+\frac{7}{3}.\frac{17}{5}& \text{Uitwerken } \\ & =px-\frac{17}{5}p-\frac{7}{3}x+\frac{119}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{-3}{3})(q+\frac{11}{17})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{17}a+1q+1.\frac{11}{17}& \text{Uitwerken } \\ & =aq+\frac{11}{17}a+1q+\frac{11}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{10}{4}+q)(p-\frac{-19}{8})& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{8}q+\frac{5}{2}p+\frac{5}{2}.\frac{19}{8}& \text{Uitwerken } \\ & =pq+\frac{19}{8}q+\frac{5}{2}p+\frac{95}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{11}{9})(\frac{-2}{4}-a)& =(\color{red}{a}+\color{orange}{\frac{11}{9}}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{11}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{2}a-\frac{11}{9}a-\frac{11}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{2})+(\frac{-11}{9}))a-\frac{11}{18} & \text{Neem samen} \\ &=-a^2-\frac{31}{18}a-\frac{11}{18} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(x+\frac{3}{18})(\frac{-8}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}x+\frac{1}{6}a-\frac{1}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}x+\frac{1}{6}a-\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-12}{12}-q)(a-\frac{5}{11})& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{11}q-1a+1.\frac{5}{11}& \text{Uitwerken } \\ & =-aq+\frac{5}{11}q-1a+\frac{5}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)