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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{19}{2})(p-\frac{10}{13})& =(\color{red}{x}+\color{orange}{\frac{19}{2}}).(\color{green}{p}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{19}{2})} . \color{green}{(p)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{13}x+\frac{19}{2}p-\frac{19}{2}.\frac{10}{13}& \text{Uitwerken } \\ & =px-\frac{10}{13}x+\frac{19}{2}p-\frac{190}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{13}x+\frac{19}{2}p-\frac{95}{13} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{10}{19})(x-5)& =(\color{red}{p}+\color{orange}{\frac{-10}{19}}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{-10}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = px-5p-\frac{10}{19}x+\frac{10}{19}.5& \text{Uitwerken } \\ & =px-5p-\frac{10}{19}x+\frac{50}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-14}{18})(x+\frac{16}{19})& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{x}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{16}{19}x+\frac{7}{9}x+\frac{7}{9}.\frac{16}{19}& \text{Uitwerken } \\ & =x^2+(\frac{16}{19}+\frac{7}{9})x+\frac{112}{171} & \text{Neem samen} \\ &=x^2+\frac{277}{171}x+\frac{112}{171} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(x+\frac{-15}{7})(\frac{-7}{12}-p)& =(\color{red}{x}+\color{orange}{\frac{-15}{7}}).(\color{green}{-p}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{12}x+\frac{15}{7}p+\frac{15}{7}.\frac{7}{12}& \text{Uitwerken } \\ & =-px-\frac{7}{12}x+\frac{15}{7}p+\frac{105}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{7}{12}x+\frac{15}{7}p+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p+\frac{-14}{18})(\frac{20}{14}-x)& =(\color{red}{p}+\color{orange}{\frac{-7}{9}}).(\color{green}{-x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{7}p+\frac{7}{9}x-\frac{7}{9}.\frac{10}{7}& \text{Uitwerken } \\ & =-px+\frac{10}{7}p+\frac{7}{9}x-\frac{70}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{10}{7}p+\frac{7}{9}x-\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a+\frac{15}{8})(b-\frac{5}{5})& =(\color{red}{a}+\color{orange}{\frac{15}{8}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a+\frac{15}{8}b-\frac{15}{8}.1& \text{Uitwerken } \\ & =ab-1a+\frac{15}{8}b-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x-\frac{-6}{3})(\frac{12}{20}+q)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{5}x+2q+2.\frac{3}{5}& \text{Uitwerken } \\ & =qx+\frac{3}{5}x+2q+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-9}{7}-p)(x-\frac{-19}{15})& =(\color{red}{-p}+\color{orange}{\frac{-9}{7}}).(\color{green}{x}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{15}p-\frac{9}{7}x-\frac{9}{7}.\frac{19}{15}& \text{Uitwerken } \\ & =-px-\frac{19}{15}p-\frac{9}{7}x-\frac{171}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{19}{15}p-\frac{9}{7}x-\frac{57}{35} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{4}{6}-b)(x-\frac{-11}{18})& =(\color{red}{-b}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{11}{18}b+\frac{2}{3}x+\frac{2}{3}.\frac{11}{18}& \text{Uitwerken } \\ & =-bx-\frac{11}{18}b+\frac{2}{3}x+\frac{22}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{11}{18}b+\frac{2}{3}x+\frac{11}{27} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{7}+p)(q+\frac{-16}{12})& =(\color{red}{p}+\color{orange}{\frac{-3}{7}}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{3}p-\frac{3}{7}q+\frac{3}{7}.\frac{4}{3}& \text{Uitwerken } \\ & =pq-\frac{4}{3}p-\frac{3}{7}q+\frac{12}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{3}p-\frac{3}{7}q+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{20}{13})(x-\frac{-3}{7})& =(\color{red}{p}+\color{orange}{\frac{20}{13}}).(\color{green}{x}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{7}p+\frac{20}{13}x+\frac{20}{13}.\frac{3}{7}& \text{Uitwerken } \\ & =px+\frac{3}{7}p+\frac{20}{13}x+\frac{60}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{9}{14}-x)(q+\frac{-6}{16})& =(\color{red}{-x}+\color{orange}{\frac{9}{14}}).(\color{green}{q}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{8}x+\frac{9}{14}q-\frac{9}{14}.\frac{3}{8}& \text{Uitwerken } \\ & =-qx+\frac{3}{8}x+\frac{9}{14}q-\frac{27}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)