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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{-5}{10})(x-\frac{-20}{18})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{10}{9}q-\frac{1}{2}x-\frac{1}{2}.\frac{10}{9}& \text{Uitwerken } \\ & =qx+\frac{10}{9}q-\frac{1}{2}x-\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{10}{9}q-\frac{1}{2}x-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{13}{4}-x)(\frac{-7}{4}-p)& =(\color{red}{-x}+\color{orange}{\frac{13}{4}}).(\color{green}{-p}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{13}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{4}x-\frac{13}{4}p-\frac{13}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =px+\frac{7}{4}x-\frac{13}{4}p-\frac{91}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{20}{10})(\frac{1}{14}-x)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{-x}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(-2)} . \color{green}{(-x)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{14}p+2x-2.\frac{1}{14}& \text{Uitwerken } \\ & =-px+\frac{1}{14}p+2x-\frac{2}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{1}{14}p+2x-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x-\frac{10}{13})(\frac{11}{20}+x)& =(\color{red}{x}+\color{orange}{\frac{-10}{13}}).(\color{green}{x}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{11}{20}x-\frac{10}{13}x-\frac{10}{13}.\frac{11}{20}& \text{Uitwerken } \\ & =x^2+(\frac{11}{20}+(\frac{-10}{13}))x-(\frac{-110}{260}) & \text{Neem samen} \\ &=x^2-\frac{57}{260}x-(\frac{-110}{260}) & \text{Maak de som} \\ &=x^2-\frac{57}{260}x+\frac{11}{26} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
5. \(\begin{align}(\frac{-10}{17}+b)(b+\frac{-13}{4})& =(\color{red}{b}+\color{orange}{\frac{-10}{17}}).(\color{green}{b}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{13}{4}b-\frac{10}{17}b+\frac{10}{17}.\frac{13}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-13}{4})+(\frac{-10}{17}))b+\frac{130}{68} & \text{Neem samen} \\ &=b^2-\frac{261}{68}b+\frac{130}{68} & \text{Maak de som} \\ &=b^2-\frac{261}{68}b+\frac{65}{34} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(\frac{-10}{16}+p)(x-\frac{-13}{19})& =(\color{red}{p}+\color{orange}{\frac{-5}{8}}).(\color{green}{x}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{19}p-\frac{5}{8}x-\frac{5}{8}.\frac{13}{19}& \text{Uitwerken } \\ & =px+\frac{13}{19}p-\frac{5}{8}x-\frac{65}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{-17}{16})(p-\frac{3}{2})& =(\color{red}{a}+\color{orange}{\frac{17}{16}}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{17}{16})} . \color{green}{(p)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}a+\frac{17}{16}p-\frac{17}{16}.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}a+\frac{17}{16}p-\frac{51}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{17}{19})(\frac{17}{18}-p)& =(\color{red}{q}+\color{orange}{\frac{-17}{19}}).(\color{green}{-p}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{18}q+\frac{17}{19}p-\frac{17}{19}.\frac{17}{18}& \text{Uitwerken } \\ & =-pq+\frac{17}{18}q+\frac{17}{19}p-\frac{289}{342} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{13}{10})(q+\frac{-8}{4})& =(\color{red}{x}+\color{orange}{\frac{-13}{10}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2x-\frac{13}{10}q+\frac{13}{10}.2& \text{Uitwerken } \\ & =qx-2x-\frac{13}{10}q+\frac{26}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-2x-\frac{13}{10}q+\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{20}+a)(x-\frac{13}{2})& =(\color{red}{a}+\color{orange}{\frac{-3}{20}}).(\color{green}{x}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{2}a-\frac{3}{20}x+\frac{3}{20}.\frac{13}{2}& \text{Uitwerken } \\ & =ax-\frac{13}{2}a-\frac{3}{20}x+\frac{39}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{8}{4})(\frac{12}{19}-b)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{12}{19}b+2b-2.\frac{12}{19}& \text{Uitwerken } \\ & =-b^2+(\frac{12}{19}+2)b-\frac{24}{19} & \text{Neem samen} \\ &=-b^2+\frac{50}{19}b-\frac{24}{19} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(x-\frac{4}{15})(\frac{-3}{12}-b)& =(\color{red}{x}+\color{orange}{\frac{-4}{15}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{4}x+\frac{4}{15}b+\frac{4}{15}.\frac{1}{4}& \text{Uitwerken } \\ & =-bx-\frac{1}{4}x+\frac{4}{15}b+\frac{4}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{1}{4}x+\frac{4}{15}b+\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)