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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{20}+q)(\frac{19}{3}+q)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{19}{3}q-\frac{1}{2}q-\frac{1}{2}.\frac{19}{3}& \text{Uitwerken } \\ & =q^2+(\frac{19}{3}+(\frac{-1}{2}))q-(\frac{-19}{6}) & \text{Neem samen} \\ &=q^2+\frac{35}{6}q-(\frac{-19}{6}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(b+\frac{-16}{5})(\frac{-1}{13}+x)& =(\color{red}{b}+\color{orange}{\frac{-16}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{13}b-\frac{16}{5}x+\frac{16}{5}.\frac{1}{13}& \text{Uitwerken } \\ & =bx-\frac{1}{13}b-\frac{16}{5}x+\frac{16}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{16}{8})(x-\frac{18}{9})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2b-2x+2.2& \text{Uitwerken } \\ & =bx-2b-2x+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{17}{10}+p)(\frac{2}{8}+x)& =(\color{red}{p}+\color{orange}{\frac{17}{10}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{17}{10})} . \color{green}{(x)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{4}p+\frac{17}{10}x+\frac{17}{10}.\frac{1}{4}& \text{Uitwerken } \\ & =px+\frac{1}{4}p+\frac{17}{10}x+\frac{17}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-2}{17}-p)(\frac{4}{20}-a)& =(\color{red}{-p}+\color{orange}{\frac{-2}{17}}).(\color{green}{-a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{5}p+\frac{2}{17}a-\frac{2}{17}.\frac{1}{5}& \text{Uitwerken } \\ & =ap-\frac{1}{5}p+\frac{2}{17}a-\frac{2}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{17}{3}-p)(\frac{-13}{15}+b)& =(\color{red}{-p}+\color{orange}{\frac{17}{3}}).(\color{green}{b}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{17}{3})} . \color{green}{(b)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{15}p+\frac{17}{3}b-\frac{17}{3}.\frac{13}{15}& \text{Uitwerken } \\ & =-bp+\frac{13}{15}p+\frac{17}{3}b-\frac{221}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{13}{15}-q)(\frac{-16}{16}-b)& =(\color{red}{-q}+\color{orange}{\frac{13}{15}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q-\frac{13}{15}b-\frac{13}{15}.1& \text{Uitwerken } \\ & =bq+1q-\frac{13}{15}b-\frac{13}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{10}{10}-b)(x+\frac{-4}{7})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{7}b+1x-1.\frac{4}{7}& \text{Uitwerken } \\ & =-bx+\frac{4}{7}b+1x-\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{11}{10})(\frac{-13}{17}+x)& =(\color{red}{q}+\color{orange}{\frac{-11}{10}}).(\color{green}{x}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{17}q-\frac{11}{10}x+\frac{11}{10}.\frac{13}{17}& \text{Uitwerken } \\ & =qx-\frac{13}{17}q-\frac{11}{10}x+\frac{143}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-13}{10})(x+\frac{-12}{20})& =(\color{red}{x}+\color{orange}{\frac{13}{10}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{5}x+\frac{13}{10}x-\frac{13}{10}.\frac{3}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{5})+\frac{13}{10})x-(\frac{-39}{50}) & \text{Neem samen} \\ &=x^2+\frac{7}{10}x-(\frac{-39}{50}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(b+\frac{-13}{14})(\frac{13}{9}+a)& =(\color{red}{b}+\color{orange}{\frac{-13}{14}}).(\color{green}{a}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{9}b-\frac{13}{14}a-\frac{13}{14}.\frac{13}{9}& \text{Uitwerken } \\ & =ab+\frac{13}{9}b-\frac{13}{14}a-\frac{169}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{-14}{13})(a-\frac{-13}{9})& =(\color{red}{b}+\color{orange}{\frac{14}{13}}).(\color{green}{a}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{14}{13})} . \color{green}{(a)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{9}b+\frac{14}{13}a+\frac{14}{13}.\frac{13}{9}& \text{Uitwerken } \\ & =ab+\frac{13}{9}b+\frac{14}{13}a+\frac{182}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{13}{9}b+\frac{14}{13}a+\frac{14}{9} & \text{Vereenvoudig} \\\end{align}\)