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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{19}{7})(p+\frac{7}{5})& =(\color{red}{x}+\color{orange}{\frac{-19}{7}}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{5}x-\frac{19}{7}p-\frac{19}{7}.\frac{7}{5}& \text{Uitwerken } \\ & =px+\frac{7}{5}x-\frac{19}{7}p-\frac{133}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{5}x-\frac{19}{7}p-\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-8}{3}-x)(p+\frac{7}{17})& =(\color{red}{-x}+\color{orange}{\frac{-8}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{17}x-\frac{8}{3}p-\frac{8}{3}.\frac{7}{17}& \text{Uitwerken } \\ & =-px-\frac{7}{17}x-\frac{8}{3}p-\frac{56}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-19}{17}+b)(\frac{3}{19}-x)& =(\color{red}{b}+\color{orange}{\frac{-19}{17}}).(\color{green}{-x}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{19}b+\frac{19}{17}x-\frac{19}{17}.\frac{3}{19}& \text{Uitwerken } \\ & =-bx+\frac{3}{19}b+\frac{19}{17}x-\frac{57}{323} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{3}{19}b+\frac{19}{17}x-\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-6}{16}+p)(\frac{18}{19}+q)& =(\color{red}{p}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{19}p-\frac{3}{8}q-\frac{3}{8}.\frac{18}{19}& \text{Uitwerken } \\ & =pq+\frac{18}{19}p-\frac{3}{8}q-\frac{54}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{18}{19}p-\frac{3}{8}q-\frac{27}{76} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{6}{15}-b)(\frac{1}{16}-x)& =(\color{red}{-b}+\color{orange}{\frac{2}{5}}).(\color{green}{-x}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{16}b-\frac{2}{5}x+\frac{2}{5}.\frac{1}{16}& \text{Uitwerken } \\ & =bx-\frac{1}{16}b-\frac{2}{5}x+\frac{2}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{16}b-\frac{2}{5}x+\frac{1}{40} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q+\frac{-10}{4})(a+\frac{-17}{20})& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{20}q-\frac{5}{2}a+\frac{5}{2}.\frac{17}{20}& \text{Uitwerken } \\ & =aq-\frac{17}{20}q-\frac{5}{2}a+\frac{85}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{17}{20}q-\frac{5}{2}a+\frac{17}{8} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q-\frac{13}{12})(\frac{11}{20}-x)& =(\color{red}{q}+\color{orange}{\frac{-13}{12}}).(\color{green}{-x}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{20}q+\frac{13}{12}x-\frac{13}{12}.\frac{11}{20}& \text{Uitwerken } \\ & =-qx+\frac{11}{20}q+\frac{13}{12}x-\frac{143}{240} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{6}{15}-q)(\frac{9}{3}+x)& =(\color{red}{-q}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(3)} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -qx-3q+\frac{2}{5}x+\frac{2}{5}.3& \text{Uitwerken } \\ & =-qx-3q+\frac{2}{5}x+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{-16}{4})(p+\frac{-12}{14})& =(\color{red}{a}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{6}{7}a+4p-4.\frac{6}{7}& \text{Uitwerken } \\ & =ap-\frac{6}{7}a+4p-\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{12}{8})(3+q)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq+3a+\frac{3}{2}q+\frac{3}{2}.3& \text{Uitwerken } \\ & =aq+3a+\frac{3}{2}q+\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{-11}{16})(\frac{12}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{11}{16}}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{11}{16})} . \color{green}{(a)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{5}q+\frac{11}{16}a+\frac{11}{16}.\frac{3}{5}& \text{Uitwerken } \\ & =aq+\frac{3}{5}q+\frac{11}{16}a+\frac{33}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a+\frac{-7}{18})(q-\frac{10}{14})& =(\color{red}{a}+\color{orange}{\frac{-7}{18}}).(\color{green}{q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{7}a-\frac{7}{18}q+\frac{7}{18}.\frac{5}{7}& \text{Uitwerken } \\ & =aq-\frac{5}{7}a-\frac{7}{18}q+\frac{35}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{7}a-\frac{7}{18}q+\frac{5}{18} & \text{Vereenvoudig} \\\end{align}\)