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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{10}{10})(\frac{6}{11}+p)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{6}{11}x-1p-1.\frac{6}{11}& \text{Uitwerken } \\ & =px+\frac{6}{11}x-1p-\frac{6}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{11}{8})(\frac{-19}{4}-a)& =(\color{red}{q}+\color{orange}{\frac{-11}{8}}).(\color{green}{-a}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{4}q+\frac{11}{8}a+\frac{11}{8}.\frac{19}{4}& \text{Uitwerken } \\ & =-aq-\frac{19}{4}q+\frac{11}{8}a+\frac{209}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{3}+p)(a+\frac{7}{11})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{11}p-\frac{2}{3}a-\frac{2}{3}.\frac{7}{11}& \text{Uitwerken } \\ & =ap+\frac{7}{11}p-\frac{2}{3}a-\frac{14}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{8}+x)(\frac{19}{15}-p)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{15}x-2p+2.\frac{19}{15}& \text{Uitwerken } \\ & =-px+\frac{19}{15}x-2p+\frac{38}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{13}{12})(\frac{15}{13}+q)& =(\color{red}{b}+\color{orange}{\frac{-13}{12}}).(\color{green}{q}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{13}b-\frac{13}{12}q-\frac{13}{12}.\frac{15}{13}& \text{Uitwerken } \\ & =bq+\frac{15}{13}b-\frac{13}{12}q-\frac{195}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{15}{13}b-\frac{13}{12}q-\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-11}{14}+p)(\frac{-17}{14}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{14}}).(\color{green}{-b}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{17}{14}p+\frac{11}{14}b+\frac{11}{14}.\frac{17}{14}& \text{Uitwerken } \\ & =-bp-\frac{17}{14}p+\frac{11}{14}b+\frac{187}{196} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{3}{8})(x-\frac{-14}{4})& =(\color{red}{b}+\color{orange}{\frac{-3}{8}}).(\color{green}{x}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{2}b-\frac{3}{8}x-\frac{3}{8}.\frac{7}{2}& \text{Uitwerken } \\ & =bx+\frac{7}{2}b-\frac{3}{8}x-\frac{21}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{9}{7}+b)(\frac{9}{12}-q)& =(\color{red}{b}+\color{orange}{\frac{9}{7}}).(\color{green}{-q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{9}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{4}b-\frac{9}{7}q+\frac{9}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =-bq+\frac{3}{4}b-\frac{9}{7}q+\frac{27}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{18}{6}+a)(p-\frac{-4}{3})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}a+3p+3.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}a+3p+\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{3}a+3p+4 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-15}{12}+a)(\frac{19}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{-x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{4}a+\frac{5}{4}x-\frac{5}{4}.\frac{19}{4}& \text{Uitwerken } \\ & =-ax+\frac{19}{4}a+\frac{5}{4}x-\frac{95}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{-9}{5})(x+\frac{3}{12})& =(\color{red}{a}+\color{orange}{\frac{-9}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{4}a-\frac{9}{5}x-\frac{9}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =ax+\frac{1}{4}a-\frac{9}{5}x-\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{15}{17})(\frac{-18}{9}-a)& =(\color{red}{q}+\color{orange}{\frac{-15}{17}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-15}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2q+\frac{15}{17}a+\frac{15}{17}.2& \text{Uitwerken } \\ & =-aq-2q+\frac{15}{17}a+\frac{30}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)