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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{19}-b)(b+\frac{12}{8})& =(\color{red}{-b}+\color{orange}{\frac{-10}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{2}b-\frac{10}{19}b-\frac{10}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{2})+(\frac{-10}{19}))b-\frac{30}{38} & \text{Neem samen} \\ &=-b^2-\frac{77}{38}b-\frac{30}{38} & \text{Maak de som} \\ &=-b^2-\frac{77}{38}b-\frac{15}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(x+\frac{-19}{17})(\frac{8}{14}+q)& =(\color{red}{x}+\color{orange}{\frac{-19}{17}}).(\color{green}{q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{7}x-\frac{19}{17}q-\frac{19}{17}.\frac{4}{7}& \text{Uitwerken } \\ & =qx+\frac{4}{7}x-\frac{19}{17}q-\frac{76}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-9}{8}-p)(\frac{-13}{12}+x)& =(\color{red}{-p}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{12}p-\frac{9}{8}x+\frac{9}{8}.\frac{13}{12}& \text{Uitwerken } \\ & =-px+\frac{13}{12}p-\frac{9}{8}x+\frac{117}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{13}{12}p-\frac{9}{8}x+\frac{39}{32} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{2}{15}+x)(\frac{5}{20}-a)& =(\color{red}{x}+\color{orange}{\frac{2}{15}}).(\color{green}{-a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{2}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{4}x-\frac{2}{15}a+\frac{2}{15}.\frac{1}{4}& \text{Uitwerken } \\ & =-ax+\frac{1}{4}x-\frac{2}{15}a+\frac{2}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{1}{4}x-\frac{2}{15}a+\frac{1}{30} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a+\frac{20}{15})(x+\frac{13}{16})& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{16}a+\frac{4}{3}x+\frac{4}{3}.\frac{13}{16}& \text{Uitwerken } \\ & =ax+\frac{13}{16}a+\frac{4}{3}x+\frac{52}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{13}{16}a+\frac{4}{3}x+\frac{13}{12} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x+\frac{12}{13})(\frac{-10}{10}+a)& =(\color{red}{x}+\color{orange}{\frac{12}{13}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{12}{13})} . \color{green}{(a)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x+\frac{12}{13}a-\frac{12}{13}.1& \text{Uitwerken } \\ & =ax-1x+\frac{12}{13}a-\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{6}{12})(\frac{9}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{17}p-\frac{1}{2}b+\frac{1}{2}.\frac{9}{17}& \text{Uitwerken } \\ & =-bp+\frac{9}{17}p-\frac{1}{2}b+\frac{9}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{8}{20})(q+\frac{-10}{10})& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p-\frac{2}{5}q+\frac{2}{5}.1& \text{Uitwerken } \\ & =pq-1p-\frac{2}{5}q+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-8)(x-\frac{-20}{2})& =(\color{red}{b}+\color{orange}{(-8)}).(\color{green}{x}+\color{blue}{10})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(10)} + \color{orange}{(-8)} . \color{green}{(x)} + \color{orange}{(-8)} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = bx+10b-8x-8.10& \text{Uitwerken } \\ & =bx+10b-8x-80 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{1}{18})(\frac{-7}{7}-x)& =(\color{red}{q}+\color{orange}{\frac{-1}{18}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{18})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1q+\frac{1}{18}x+\frac{1}{18}.1& \text{Uitwerken } \\ & =-qx-1q+\frac{1}{18}x+\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{19}{8}+a)(x+\frac{-12}{9})& =(\color{red}{a}+\color{orange}{\frac{19}{8}}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{3}a+\frac{19}{8}x-\frac{19}{8}.\frac{4}{3}& \text{Uitwerken } \\ & =ax-\frac{4}{3}a+\frac{19}{8}x-\frac{76}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{4}{3}a+\frac{19}{8}x-\frac{19}{6} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-16}{11}+x)(\frac{-13}{2}+p)& =(\color{red}{x}+\color{orange}{\frac{-16}{11}}).(\color{green}{p}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{2}x-\frac{16}{11}p+\frac{16}{11}.\frac{13}{2}& \text{Uitwerken } \\ & =px-\frac{13}{2}x-\frac{16}{11}p+\frac{208}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{13}{2}x-\frac{16}{11}p+\frac{104}{11} & \text{Vereenvoudig} \\\end{align}\)