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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-3}{18})(\frac{-14}{14}+q)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a+\frac{1}{6}q-\frac{1}{6}.1& \text{Uitwerken } \\ & =aq-1a+\frac{1}{6}q-\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{6}{2})(x+20)& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{20})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(20)} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = px+20p-3x-3.20& \text{Uitwerken } \\ & =px+20p-3x-60 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{-3}{14})(\frac{-3}{13}-x)& =(\color{red}{b}+\color{orange}{\frac{3}{14}}).(\color{green}{-x}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(\frac{3}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{13}b-\frac{3}{14}x-\frac{3}{14}.\frac{3}{13}& \text{Uitwerken } \\ & =-bx-\frac{3}{13}b-\frac{3}{14}x-\frac{9}{182} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-(-1))(x-\frac{-19}{3})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{3}b+1x+1.\frac{19}{3}& \text{Uitwerken } \\ & =bx+\frac{19}{3}b+1x+\frac{19}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-18}{7}+p)(\frac{-2}{9}+a)& =(\color{red}{p}+\color{orange}{\frac{-18}{7}}).(\color{green}{a}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{9}p-\frac{18}{7}a+\frac{18}{7}.\frac{2}{9}& \text{Uitwerken } \\ & =ap-\frac{2}{9}p-\frac{18}{7}a+\frac{36}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{9}p-\frac{18}{7}a+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a+\frac{7}{17})(16+x)& =(\color{red}{a}+\color{orange}{\frac{7}{17}}).(\color{green}{x}+\color{blue}{16})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(16)} + \color{orange}{(\frac{7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = ax+16a+\frac{7}{17}x+\frac{7}{17}.16& \text{Uitwerken } \\ & =ax+16a+\frac{7}{17}x+\frac{112}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{-11}{13})(\frac{-12}{12}+p)& =(\color{red}{x}+\color{orange}{\frac{-11}{13}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x-\frac{11}{13}p+\frac{11}{13}.1& \text{Uitwerken } \\ & =px-1x-\frac{11}{13}p+\frac{11}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{1}{5}-p)(b+\frac{8}{10})& =(\color{red}{-p}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{5}p+\frac{1}{5}b+\frac{1}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-bp-\frac{4}{5}p+\frac{1}{5}b+\frac{4}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{-11}{8})(b-\frac{6}{13})& =(\color{red}{x}+\color{orange}{\frac{11}{8}}).(\color{green}{b}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{6}{13}x+\frac{11}{8}b-\frac{11}{8}.\frac{6}{13}& \text{Uitwerken } \\ & =bx-\frac{6}{13}x+\frac{11}{8}b-\frac{66}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{6}{13}x+\frac{11}{8}b-\frac{33}{52} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-10}{11}+a)(q+\frac{5}{10})& =(\color{red}{a}+\color{orange}{\frac{-10}{11}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{2}a-\frac{10}{11}q-\frac{10}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =aq+\frac{1}{2}a-\frac{10}{11}q-\frac{10}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{2}a-\frac{10}{11}q-\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-6}{16}+a)(\frac{-13}{6}-p)& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{-p}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{6}a+\frac{3}{8}p+\frac{3}{8}.\frac{13}{6}& \text{Uitwerken } \\ & =-ap-\frac{13}{6}a+\frac{3}{8}p+\frac{39}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{13}{6}a+\frac{3}{8}p+\frac{13}{16} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a+\frac{19}{15})(x+\frac{6}{6})& =(\color{red}{a}+\color{orange}{\frac{19}{15}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{19}{15})} . \color{green}{(x)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a+\frac{19}{15}x+\frac{19}{15}.1& \text{Uitwerken } \\ & =ax+1a+\frac{19}{15}x+\frac{19}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)