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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-14}{5}+q)(\frac{-9}{14}-x)& =(\color{red}{q}+\color{orange}{\frac{-14}{5}}).(\color{green}{-x}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{9}{14}q+\frac{14}{5}x+\frac{14}{5}.\frac{9}{14}& \text{Uitwerken } \\ & =-qx-\frac{9}{14}q+\frac{14}{5}x+\frac{126}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{9}{14}q+\frac{14}{5}x+\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a-\frac{1}{10})(p-\frac{10}{7})& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{7}a-\frac{1}{10}p+\frac{1}{10}.\frac{10}{7}& \text{Uitwerken } \\ & =ap-\frac{10}{7}a-\frac{1}{10}p+\frac{10}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{7}a-\frac{1}{10}p+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{19}{6})(p-\frac{-12}{19})& =(\color{red}{x}+\color{orange}{\frac{-19}{6}}).(\color{green}{p}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{12}{19}x-\frac{19}{6}p-\frac{19}{6}.\frac{12}{19}& \text{Uitwerken } \\ & =px+\frac{12}{19}x-\frac{19}{6}p-\frac{228}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{12}{19}x-\frac{19}{6}p-2 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{10}{4}-q)(b+\frac{9}{14})& =(\color{red}{-q}+\color{orange}{\frac{5}{2}}).(\color{green}{b}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{14}q+\frac{5}{2}b+\frac{5}{2}.\frac{9}{14}& \text{Uitwerken } \\ & =-bq-\frac{9}{14}q+\frac{5}{2}b+\frac{45}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{1}{12})(b+\frac{17}{5})& =(\color{red}{q}+\color{orange}{\frac{-1}{12}}).(\color{green}{b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{5}q-\frac{1}{12}b-\frac{1}{12}.\frac{17}{5}& \text{Uitwerken } \\ & =bq+\frac{17}{5}q-\frac{1}{12}b-\frac{17}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-3}{6}-x)(b+\frac{-18}{6})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bx+3x-\frac{1}{2}b+\frac{1}{2}.3& \text{Uitwerken } \\ & =-bx+3x-\frac{1}{2}b+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{19}{16})(\frac{15}{6}-b)& =(\color{red}{q}+\color{orange}{\frac{19}{16}}).(\color{green}{-b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{19}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{2}q-\frac{19}{16}b+\frac{19}{16}.\frac{5}{2}& \text{Uitwerken } \\ & =-bq+\frac{5}{2}q-\frac{19}{16}b+\frac{95}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-5)(a-\frac{-18}{13})& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{a}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(-5)} . \color{green}{(a)} + \color{orange}{(-5)} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{18}{13}b-5a-5.\frac{18}{13}& \text{Uitwerken } \\ & =ab+\frac{18}{13}b-5a-\frac{90}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{4}{17})(a+\frac{-19}{7})& =(\color{red}{a}+\color{orange}{\frac{-4}{17}}).(\color{green}{a}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{7}a-\frac{4}{17}a+\frac{4}{17}.\frac{19}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{7})+(\frac{-4}{17}))a+\frac{76}{119} & \text{Neem samen} \\ &=a^2-\frac{351}{119}a+\frac{76}{119} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a+\frac{-6}{15})(p-\frac{18}{2})& =(\color{red}{a}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = ap-9a-\frac{2}{5}p+\frac{2}{5}.9& \text{Uitwerken } \\ & =ap-9a-\frac{2}{5}p+\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{-15}{19})(a-\frac{-6}{6})& =(\color{red}{b}+\color{orange}{\frac{15}{19}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{15}{19})} . \color{green}{(a)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b+\frac{15}{19}a+\frac{15}{19}.1& \text{Uitwerken } \\ & =ab+1b+\frac{15}{19}a+\frac{15}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{17}{11})(x+\frac{17}{11})& =(\color{red}{q}+\color{orange}{\frac{-17}{11}}).(\color{green}{x}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{11}q-\frac{17}{11}x-\frac{17}{11}.\frac{17}{11}& \text{Uitwerken } \\ & =qx+\frac{17}{11}q-\frac{17}{11}x-\frac{289}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)