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

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

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Verbetersleutel

1. \(\begin{align}(\frac{13}{10}+a)(\frac{-3}{5}-b)& =(\color{red}{a}+\color{orange}{\frac{13}{10}}).(\color{green}{-b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{13}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{5}a-\frac{13}{10}b-\frac{13}{10}.\frac{3}{5}& \text{Uitwerken } \\ & =-ab-\frac{3}{5}a-\frac{13}{10}b-\frac{39}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{11}{8})(x+\frac{20}{16})& =(\color{red}{b}+\color{orange}{\frac{-11}{8}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{4}b-\frac{11}{8}x-\frac{11}{8}.\frac{5}{4}& \text{Uitwerken } \\ & =bx+\frac{5}{4}b-\frac{11}{8}x-\frac{55}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{6}{19}+a)(p+\frac{-8}{8})& =(\color{red}{a}+\color{orange}{\frac{6}{19}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{6}{19})} . \color{green}{(p)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a+\frac{6}{19}p-\frac{6}{19}.1& \text{Uitwerken } \\ & =ap-1a+\frac{6}{19}p-\frac{6}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{18}{7})(\frac{-15}{9}+q)& =(\color{red}{a}+\color{orange}{\frac{-18}{7}}).(\color{green}{q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{3}a-\frac{18}{7}q+\frac{18}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =aq-\frac{5}{3}a-\frac{18}{7}q+\frac{90}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{3}a-\frac{18}{7}q+\frac{30}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{9}+x)(p-\frac{-14}{13})& =(\color{red}{x}+\color{orange}{\frac{-16}{9}}).(\color{green}{p}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{13}x-\frac{16}{9}p-\frac{16}{9}.\frac{14}{13}& \text{Uitwerken } \\ & =px+\frac{14}{13}x-\frac{16}{9}p-\frac{224}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-9}{19}+p)(\frac{20}{13}-q)& =(\color{red}{p}+\color{orange}{\frac{-9}{19}}).(\color{green}{-q}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{20}{13}p+\frac{9}{19}q-\frac{9}{19}.\frac{20}{13}& \text{Uitwerken } \\ & =-pq+\frac{20}{13}p+\frac{9}{19}q-\frac{180}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{8}{5})((-2)-b)& =(\color{red}{q}+\color{orange}{\frac{8}{5}}).(\color{green}{-b}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{8}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bq-2q-\frac{8}{5}b-\frac{8}{5}.2& \text{Uitwerken } \\ & =-bq-2q-\frac{8}{5}b-\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{11}{7}+q)(\frac{-13}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{11}{7}}).(\color{green}{a}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{11}{7})} . \color{green}{(a)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{20}q+\frac{11}{7}a-\frac{11}{7}.\frac{13}{20}& \text{Uitwerken } \\ & =aq-\frac{13}{20}q+\frac{11}{7}a-\frac{143}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{12}{6}-b)(x-\frac{1}{12})& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{12}b+2x-2.\frac{1}{12}& \text{Uitwerken } \\ & =-bx+\frac{1}{12}b+2x-\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{1}{12}b+2x-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{-17}{2})(11-x)& =(\color{red}{p}+\color{orange}{\frac{17}{2}}).(\color{green}{-x}+\color{blue}{11})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(11)} + \color{orange}{(\frac{17}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -px+11p-\frac{17}{2}x+\frac{17}{2}.11& \text{Uitwerken } \\ & =-px+11p-\frac{17}{2}x+\frac{187}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{12}-q)(a+\frac{7}{19})& =(\color{red}{-q}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{19}q-\frac{7}{12}a-\frac{7}{12}.\frac{7}{19}& \text{Uitwerken } \\ & =-aq-\frac{7}{19}q-\frac{7}{12}a-\frac{49}{228} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{-15}{12})(\frac{-1}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{20}q-\frac{5}{4}a+\frac{5}{4}.\frac{1}{20}& \text{Uitwerken } \\ & =aq-\frac{1}{20}q-\frac{5}{4}a+\frac{5}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{20}q-\frac{5}{4}a+\frac{1}{16} & \text{Vereenvoudig} \\\end{align}\)