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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{-3}{8})(b-\frac{9}{18})& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}x-\frac{3}{8}b+\frac{3}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}x-\frac{3}{8}b+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-15}{7}-x)(a-\frac{-15}{13})& =(\color{red}{-x}+\color{orange}{\frac{-15}{7}}).(\color{green}{a}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{13}x-\frac{15}{7}a-\frac{15}{7}.\frac{15}{13}& \text{Uitwerken } \\ & =-ax-\frac{15}{13}x-\frac{15}{7}a-\frac{225}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{-4}{18})(x+\frac{1}{9})& =(\color{red}{q}+\color{orange}{\frac{-2}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{9}q-\frac{2}{9}x-\frac{2}{9}.\frac{1}{9}& \text{Uitwerken } \\ & =qx+\frac{1}{9}q-\frac{2}{9}x-\frac{2}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+(-2))(x+\frac{-17}{20})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{20}p-2x+2.\frac{17}{20}& \text{Uitwerken } \\ & =px-\frac{17}{20}p-2x+\frac{34}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{20}p-2x+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a-\frac{-9}{12})(x-\frac{-9}{11})& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{11}a+\frac{3}{4}x+\frac{3}{4}.\frac{9}{11}& \text{Uitwerken } \\ & =ax+\frac{9}{11}a+\frac{3}{4}x+\frac{27}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{2}{4}-x)(a-7)& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{(-7)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-7)} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -ax+7x+\frac{1}{2}a-\frac{1}{2}.7& \text{Uitwerken } \\ & =-ax+7x+\frac{1}{2}a-\frac{7}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{4}+q)(a-\frac{13}{15})& =(\color{red}{q}+\color{orange}{\frac{-13}{4}}).(\color{green}{a}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{15}q-\frac{13}{4}a+\frac{13}{4}.\frac{13}{15}& \text{Uitwerken } \\ & =aq-\frac{13}{15}q-\frac{13}{4}a+\frac{169}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-13}{15}-b)(\frac{-19}{16}+b)& =(\color{red}{-b}+\color{orange}{\frac{-13}{15}}).(\color{green}{b}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{19}{16}b-\frac{13}{15}b+\frac{13}{15}.\frac{19}{16}& \text{Uitwerken } \\ & =-b^2+(\frac{19}{16}+(\frac{-13}{15}))b+(\frac{-247}{240}) & \text{Neem samen} \\ &=-b^2+\frac{77}{240}b+(\frac{-247}{240}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{-1}{10}+x)(q-\frac{10}{16})& =(\color{red}{x}+\color{orange}{\frac{-1}{10}}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{8}x-\frac{1}{10}q+\frac{1}{10}.\frac{5}{8}& \text{Uitwerken } \\ & =qx-\frac{5}{8}x-\frac{1}{10}q+\frac{5}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{8}x-\frac{1}{10}q+\frac{1}{16} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{20}{4})(b+\frac{14}{6})& =(\color{red}{p}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{3}p+5b+5.\frac{7}{3}& \text{Uitwerken } \\ & =bp+\frac{7}{3}p+5b+\frac{35}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{16}{11}+a)(\frac{-10}{11}+q)& =(\color{red}{a}+\color{orange}{\frac{16}{11}}).(\color{green}{q}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{11}a+\frac{16}{11}q-\frac{16}{11}.\frac{10}{11}& \text{Uitwerken } \\ & =aq-\frac{10}{11}a+\frac{16}{11}q-\frac{160}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{-3}{17})(\frac{-1}{17}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{3}{17})} . \color{green}{(x)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{17}x+\frac{3}{17}x-\frac{3}{17}.\frac{1}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{17})+\frac{3}{17})x-(\frac{-3}{289}) & \text{Neem samen} \\ &=x^2+\frac{2}{17}x-(\frac{-3}{289}) & \text{Maak de som} \\\end{align}\)