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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-9}{14})(p-\frac{9}{18})& =(\color{red}{a}+\color{orange}{\frac{-9}{14}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{2}a-\frac{9}{14}p+\frac{9}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =ap-\frac{1}{2}a-\frac{9}{14}p+\frac{9}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-7}{14}-x)(\frac{-5}{17}-p)& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{-p}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{17}x+\frac{1}{2}p+\frac{1}{2}.\frac{5}{17}& \text{Uitwerken } \\ & =px+\frac{5}{17}x+\frac{1}{2}p+\frac{5}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{-10}{15})(a-\frac{-16}{8})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2b+\frac{2}{3}a+\frac{2}{3}.2& \text{Uitwerken } \\ & =ab+2b+\frac{2}{3}a+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{17}{19}+q)(q+\frac{11}{19})& =(\color{red}{q}+\color{orange}{\frac{17}{19}}).(\color{green}{q}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{17}{19})} . \color{green}{(q)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{19}q+\frac{17}{19}q+\frac{17}{19}.\frac{11}{19}& \text{Uitwerken } \\ & =q^2+(\frac{11}{19}+\frac{17}{19})q+\frac{187}{361} & \text{Neem samen} \\ &=q^2+\frac{28}{19}q+\frac{187}{361} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(12+p)(p-9)& =(\color{red}{p}+\color{orange}{12}).(\color{green}{p}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-9)} + \color{orange}{(12)} . \color{green}{(p)} + \color{orange}{(12)} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = pp-9p+12p-12.9& \text{Uitwerken } \\ & =p^2+((-9)+12)p-(-108) & \text{Neem samen} \\ &=p^2+3p-(-108) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-3}{13}-q)(x+\frac{19}{20})& =(\color{red}{-q}+\color{orange}{\frac{-3}{13}}).(\color{green}{x}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{20}q-\frac{3}{13}x-\frac{3}{13}.\frac{19}{20}& \text{Uitwerken } \\ & =-qx-\frac{19}{20}q-\frac{3}{13}x-\frac{57}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{16}{16})(a-\frac{1}{17})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{17}p+1a-1.\frac{1}{17}& \text{Uitwerken } \\ & =ap-\frac{1}{17}p+1a-\frac{1}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{17}{2})(p-\frac{8}{18})& =(\color{red}{x}+\color{orange}{\frac{17}{2}}).(\color{green}{p}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{17}{2})} . \color{green}{(p)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{9}x+\frac{17}{2}p-\frac{17}{2}.\frac{4}{9}& \text{Uitwerken } \\ & =px-\frac{4}{9}x+\frac{17}{2}p-\frac{68}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{9}x+\frac{17}{2}p-\frac{34}{9} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-12}{20}-a)(\frac{19}{5}-b)& =(\color{red}{-a}+\color{orange}{\frac{-3}{5}}).(\color{green}{-b}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{5}a+\frac{3}{5}b-\frac{3}{5}.\frac{19}{5}& \text{Uitwerken } \\ & =ab-\frac{19}{5}a+\frac{3}{5}b-\frac{57}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-8}{12}+p)(x-\frac{16}{5})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{5}p-\frac{2}{3}x+\frac{2}{3}.\frac{16}{5}& \text{Uitwerken } \\ & =px-\frac{16}{5}p-\frac{2}{3}x+\frac{32}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-8)(\frac{4}{3}+p)& =(\color{red}{a}+\color{orange}{(-8)}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-8)} . \color{green}{(p)} + \color{orange}{(-8)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}a-8p-8.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}a-8p-\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{17}{6})(a+\frac{-12}{14})& =(\color{red}{x}+\color{orange}{\frac{17}{6}}).(\color{green}{a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{17}{6})} . \color{green}{(a)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{6}{7}x+\frac{17}{6}a-\frac{17}{6}.\frac{6}{7}& \text{Uitwerken } \\ & =ax-\frac{6}{7}x+\frac{17}{6}a-\frac{102}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{6}{7}x+\frac{17}{6}a-\frac{17}{7} & \text{Vereenvoudig} \\\end{align}\)