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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-12}{12})(\frac{-16}{4}-b)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ab-4a-1b-1.4& \text{Uitwerken } \\ & =-ab-4a-1b-4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{5}{5}+a)(\frac{10}{5}-p)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap+2a-1p+1.2& \text{Uitwerken } \\ & =-ap+2a-1p+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-7}{15}-q)(p+\frac{-19}{7})& =(\color{red}{-q}+\color{orange}{\frac{-7}{15}}).(\color{green}{p}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{19}{7}q-\frac{7}{15}p+\frac{7}{15}.\frac{19}{7}& \text{Uitwerken } \\ & =-pq+\frac{19}{7}q-\frac{7}{15}p+\frac{133}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{19}{7}q-\frac{7}{15}p+\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b+\frac{-18}{17})(\frac{-3}{14}+b)& =(\color{red}{b}+\color{orange}{\frac{-18}{17}}).(\color{green}{b}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{14}b-\frac{18}{17}b+\frac{18}{17}.\frac{3}{14}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{14})+(\frac{-18}{17}))b+\frac{54}{238} & \text{Neem samen} \\ &=b^2-\frac{303}{238}b+\frac{54}{238} & \text{Maak de som} \\ &=b^2-\frac{303}{238}b+\frac{27}{119} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{-18}{10}+q)(p+\frac{6}{5})& =(\color{red}{q}+\color{orange}{\frac{-9}{5}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{5}q-\frac{9}{5}p-\frac{9}{5}.\frac{6}{5}& \text{Uitwerken } \\ & =pq+\frac{6}{5}q-\frac{9}{5}p-\frac{54}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-11}{13}+a)(\frac{-17}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{-11}{13}}).(\color{green}{p}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{4}a-\frac{11}{13}p+\frac{11}{13}.\frac{17}{4}& \text{Uitwerken } \\ & =ap-\frac{17}{4}a-\frac{11}{13}p+\frac{187}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+18)(x+\frac{-14}{14})& =(\color{red}{a}+\color{orange}{18}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+18x-18.1& \text{Uitwerken } \\ & =ax-1a+18x-18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{3}{7}-p)(a+\frac{11}{19})& =(\color{red}{-p}+\color{orange}{\frac{3}{7}}).(\color{green}{a}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{19}p+\frac{3}{7}a+\frac{3}{7}.\frac{11}{19}& \text{Uitwerken } \\ & =-ap-\frac{11}{19}p+\frac{3}{7}a+\frac{33}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{7}{16})(x+\frac{9}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{16}}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{7}{16})} . \color{green}{(x)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{5}p+\frac{7}{16}x+\frac{7}{16}.\frac{9}{5}& \text{Uitwerken } \\ & =px+\frac{9}{5}p+\frac{7}{16}x+\frac{63}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-19}{12})(x+\frac{17}{6})& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{x}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{6}a-\frac{19}{12}x-\frac{19}{12}.\frac{17}{6}& \text{Uitwerken } \\ & =ax+\frac{17}{6}a-\frac{19}{12}x-\frac{323}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-7}{7})(\frac{-13}{12}-b)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{12}x-1b-1.\frac{13}{12}& \text{Uitwerken } \\ & =-bx-\frac{13}{12}x-1b-\frac{13}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-4}{6}-q)(p+\frac{-3}{8})& =(\color{red}{-q}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{8}q-\frac{2}{3}p+\frac{2}{3}.\frac{3}{8}& \text{Uitwerken } \\ & =-pq+\frac{3}{8}q-\frac{2}{3}p+\frac{6}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{3}{8}q-\frac{2}{3}p+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)