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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-12}{17})(b-\frac{8}{9})& =(\color{red}{p}+\color{orange}{\frac{12}{17}}).(\color{green}{b}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{12}{17})} . \color{green}{(b)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{9}p+\frac{12}{17}b-\frac{12}{17}.\frac{8}{9}& \text{Uitwerken } \\ & =bp-\frac{8}{9}p+\frac{12}{17}b-\frac{96}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{8}{9}p+\frac{12}{17}b-\frac{32}{51} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-4}{13}-b)(b+\frac{-3}{8})& =(\color{red}{-b}+\color{orange}{\frac{-4}{13}}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{3}{8}b-\frac{4}{13}b+\frac{4}{13}.\frac{3}{8}& \text{Uitwerken } \\ & =-b^2+(\frac{3}{8}+(\frac{-4}{13}))b+(\frac{-12}{104}) & \text{Neem samen} \\ &=-b^2+\frac{7}{104}b+(\frac{-12}{104}) & \text{Maak de som} \\ &=-b^2+\frac{7}{104}b+(\frac{-3}{26}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(b-\frac{-4}{2})(\frac{4}{7}+x)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{7}b+2x+2.\frac{4}{7}& \text{Uitwerken } \\ & =bx+\frac{4}{7}b+2x+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-6}{16}+p)(b+\frac{14}{8})& =(\color{red}{p}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{4}p-\frac{3}{8}b-\frac{3}{8}.\frac{7}{4}& \text{Uitwerken } \\ & =bp+\frac{7}{4}p-\frac{3}{8}b-\frac{21}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-19}{3}+b)(\frac{1}{6}-p)& =(\color{red}{b}+\color{orange}{\frac{-19}{3}}).(\color{green}{-p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{6}b+\frac{19}{3}p-\frac{19}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =-bp+\frac{1}{6}b+\frac{19}{3}p-\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-16}{8}+q)(a+\frac{-10}{20})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{2}q-2a+2.\frac{1}{2}& \text{Uitwerken } \\ & =aq-\frac{1}{2}q-2a+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{2}q-2a+1 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{15}-q)(x-\frac{-2}{12})& =(\color{red}{-q}+\color{orange}{\frac{-1}{15}}).(\color{green}{x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{6}q-\frac{1}{15}x-\frac{1}{15}.\frac{1}{6}& \text{Uitwerken } \\ & =-qx-\frac{1}{6}q-\frac{1}{15}x-\frac{1}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{18}{4}+q)(a+\frac{1}{13})& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{9}{2})} . \color{green}{(a)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{13}q+\frac{9}{2}a+\frac{9}{2}.\frac{1}{13}& \text{Uitwerken } \\ & =aq+\frac{1}{13}q+\frac{9}{2}a+\frac{9}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-11}{13}+q)(\frac{-4}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{5}q-\frac{11}{13}b+\frac{11}{13}.\frac{4}{5}& \text{Uitwerken } \\ & =bq-\frac{4}{5}q-\frac{11}{13}b+\frac{44}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{12}{18}-q)(x+\frac{2}{11})& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{11}q+\frac{2}{3}x+\frac{2}{3}.\frac{2}{11}& \text{Uitwerken } \\ & =-qx-\frac{2}{11}q+\frac{2}{3}x+\frac{4}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{13}{11})(p+\frac{15}{11})& =(\color{red}{x}+\color{orange}{\frac{13}{11}}).(\color{green}{p}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{13}{11})} . \color{green}{(p)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{15}{11}x+\frac{13}{11}p+\frac{13}{11}.\frac{15}{11}& \text{Uitwerken } \\ & =px+\frac{15}{11}x+\frac{13}{11}p+\frac{195}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{16}{14}+x)(\frac{10}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{2}x+\frac{8}{7}q+\frac{8}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =qx+\frac{5}{2}x+\frac{8}{7}q+\frac{40}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{2}x+\frac{8}{7}q+\frac{20}{7} & \text{Vereenvoudig} \\\end{align}\)