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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-13}{4})(\frac{-10}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{-13}{4}}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{2}a-\frac{13}{4}p+\frac{13}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =ap-\frac{5}{2}a-\frac{13}{4}p+\frac{65}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{9}{15})(\frac{7}{2}-p)& =(\color{red}{x}+\color{orange}{\frac{3}{5}}).(\color{green}{-p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{2}x-\frac{3}{5}p+\frac{3}{5}.\frac{7}{2}& \text{Uitwerken } \\ & =-px+\frac{7}{2}x-\frac{3}{5}p+\frac{21}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-8}{12})(\frac{1}{20}-b)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{-b}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{20}p+\frac{2}{3}b-\frac{2}{3}.\frac{1}{20}& \text{Uitwerken } \\ & =-bp+\frac{1}{20}p+\frac{2}{3}b-\frac{2}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{20}p+\frac{2}{3}b-\frac{1}{30} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b+\frac{19}{20})(p+\frac{-2}{7})& =(\color{red}{b}+\color{orange}{\frac{19}{20}}).(\color{green}{p}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{19}{20})} . \color{green}{(p)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{7}b+\frac{19}{20}p-\frac{19}{20}.\frac{2}{7}& \text{Uitwerken } \\ & =bp-\frac{2}{7}b+\frac{19}{20}p-\frac{38}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{2}{7}b+\frac{19}{20}p-\frac{19}{70} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x-\frac{1}{6})(a+\frac{-5}{17})& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{17}x-\frac{1}{6}a+\frac{1}{6}.\frac{5}{17}& \text{Uitwerken } \\ & =ax-\frac{5}{17}x-\frac{1}{6}a+\frac{5}{102} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{15}{10}-q)(q-15)& =(\color{red}{-q}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{(-15)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-15)} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -qq+15q+\frac{3}{2}q-\frac{3}{2}.15& \text{Uitwerken } \\ & =-q^2+(15+\frac{3}{2})q-\frac{45}{2} & \text{Neem samen} \\ &=-q^2+\frac{33}{2}q-\frac{45}{2} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(b-\frac{3}{12})(a+\frac{-7}{5})& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{5}b-\frac{1}{4}a+\frac{1}{4}.\frac{7}{5}& \text{Uitwerken } \\ & =ab-\frac{7}{5}b-\frac{1}{4}a+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-15}{13}-p)(x-\frac{19}{11})& =(\color{red}{-p}+\color{orange}{\frac{-15}{13}}).(\color{green}{x}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{11}p-\frac{15}{13}x+\frac{15}{13}.\frac{19}{11}& \text{Uitwerken } \\ & =-px+\frac{19}{11}p-\frac{15}{13}x+\frac{285}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{-1}{5})(\frac{-15}{17}+p)& =(\color{red}{a}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{17}a+\frac{1}{5}p-\frac{1}{5}.\frac{15}{17}& \text{Uitwerken } \\ & =ap-\frac{15}{17}a+\frac{1}{5}p-\frac{15}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{15}{17}a+\frac{1}{5}p-\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{19}{20})(\frac{-12}{4}+b)& =(\color{red}{a}+\color{orange}{\frac{-19}{20}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-19}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ab-3a-\frac{19}{20}b+\frac{19}{20}.3& \text{Uitwerken } \\ & =ab-3a-\frac{19}{20}b+\frac{57}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{3}{18})(\frac{-19}{13}-a)& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{-a}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{19}{13}a+\frac{1}{6}a+\frac{1}{6}.\frac{19}{13}& \text{Uitwerken } \\ & =-a^2+((\frac{-19}{13})+\frac{1}{6})a+(\frac{-19}{78}) & \text{Neem samen} \\ &=-a^2-\frac{101}{78}a+(\frac{-19}{78}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{16}{12}-b)(\frac{13}{20}-q)& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{-q}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{20}b-\frac{4}{3}q+\frac{4}{3}.\frac{13}{20}& \text{Uitwerken } \\ & =bq-\frac{13}{20}b-\frac{4}{3}q+\frac{52}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{20}b-\frac{4}{3}q+\frac{13}{15} & \text{Vereenvoudig} \\\end{align}\)