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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{10}{20})(\frac{-17}{14}-x)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{14}q-\frac{1}{2}x-\frac{1}{2}.\frac{17}{14}& \text{Uitwerken } \\ & =-qx-\frac{17}{14}q-\frac{1}{2}x-\frac{17}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{4}{12}-q)(\frac{7}{3}-p)& =(\color{red}{-q}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{3}q-\frac{1}{3}p+\frac{1}{3}.\frac{7}{3}& \text{Uitwerken } \\ & =pq-\frac{7}{3}q-\frac{1}{3}p+\frac{7}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a-\frac{-19}{11})(\frac{14}{3}-q)& =(\color{red}{a}+\color{orange}{\frac{19}{11}}).(\color{green}{-q}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{19}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{14}{3}a-\frac{19}{11}q+\frac{19}{11}.\frac{14}{3}& \text{Uitwerken } \\ & =-aq+\frac{14}{3}a-\frac{19}{11}q+\frac{266}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{13}{6})(\frac{-11}{3}-p)& =(\color{red}{q}+\color{orange}{\frac{-13}{6}}).(\color{green}{-p}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{3}q+\frac{13}{6}p+\frac{13}{6}.\frac{11}{3}& \text{Uitwerken } \\ & =-pq-\frac{11}{3}q+\frac{13}{6}p+\frac{143}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-(-2))(a-\frac{-1}{16})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{16}x+2a+2.\frac{1}{16}& \text{Uitwerken } \\ & =ax+\frac{1}{16}x+2a+\frac{2}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{16}x+2a+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a-\frac{2}{15})(\frac{-3}{14}+x)& =(\color{red}{a}+\color{orange}{\frac{-2}{15}}).(\color{green}{x}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{14}a-\frac{2}{15}x+\frac{2}{15}.\frac{3}{14}& \text{Uitwerken } \\ & =ax-\frac{3}{14}a-\frac{2}{15}x+\frac{6}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{14}a-\frac{2}{15}x+\frac{1}{35} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{10}+p)(b-\frac{-9}{13})& =(\color{red}{p}+\color{orange}{\frac{-13}{10}}).(\color{green}{b}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{13}p-\frac{13}{10}b-\frac{13}{10}.\frac{9}{13}& \text{Uitwerken } \\ & =bp+\frac{9}{13}p-\frac{13}{10}b-\frac{117}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{13}p-\frac{13}{10}b-\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{6}{11})(\frac{-12}{4}-b)& =(\color{red}{q}+\color{orange}{\frac{-6}{11}}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{-6}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bq-3q+\frac{6}{11}b+\frac{6}{11}.3& \text{Uitwerken } \\ & =-bq-3q+\frac{6}{11}b+\frac{18}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-10}{16})(x+19)& =(\color{red}{x}+\color{orange}{\frac{-5}{8}}).(\color{green}{x}+\color{blue}{19})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(19)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = xx+19x-\frac{5}{8}x-\frac{5}{8}.19& \text{Uitwerken } \\ & =x^2+(19+(\frac{-5}{8}))x-(\frac{-95}{8}) & \text{Neem samen} \\ &=x^2+\frac{147}{8}x-(\frac{-95}{8}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a+\frac{13}{20})(x-\frac{-4}{6})& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}a+\frac{13}{20}x+\frac{13}{20}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}a+\frac{13}{20}x+\frac{26}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}a+\frac{13}{20}x+\frac{13}{30} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{8}{19}+q)(\frac{16}{9}-x)& =(\color{red}{q}+\color{orange}{\frac{8}{19}}).(\color{green}{-x}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{8}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{16}{9}q-\frac{8}{19}x+\frac{8}{19}.\frac{16}{9}& \text{Uitwerken } \\ & =-qx+\frac{16}{9}q-\frac{8}{19}x+\frac{128}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(20-a)(\frac{-3}{7}-x)& =(\color{red}{-a}+\color{orange}{20}).(\color{green}{-x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(20)} . \color{green}{(-x)} + \color{orange}{(20)} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{7}a-20x-20.\frac{3}{7}& \text{Uitwerken } \\ & =ax+\frac{3}{7}a-20x-\frac{60}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)