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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{10}{11})(q-(-14))& =(\color{red}{q}+\color{orange}{\frac{10}{11}}).(\color{green}{q}+\color{blue}{14})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(14)} + \color{orange}{(\frac{10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = qq+14q+\frac{10}{11}q+\frac{10}{11}.14& \text{Uitwerken } \\ & =q^2+(14+\frac{10}{11})q+\frac{140}{11} & \text{Neem samen} \\ &=q^2+\frac{164}{11}q+\frac{140}{11} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(b-\frac{-6}{7})(x-\frac{17}{15})& =(\color{red}{b}+\color{orange}{\frac{6}{7}}).(\color{green}{x}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{6}{7})} . \color{green}{(x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{15}b+\frac{6}{7}x-\frac{6}{7}.\frac{17}{15}& \text{Uitwerken } \\ & =bx-\frac{17}{15}b+\frac{6}{7}x-\frac{102}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{17}{15}b+\frac{6}{7}x-\frac{34}{35} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b-\frac{-4}{10})(q-\frac{-14}{20})& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{10}b+\frac{2}{5}q+\frac{2}{5}.\frac{7}{10}& \text{Uitwerken } \\ & =bq+\frac{7}{10}b+\frac{2}{5}q+\frac{14}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{10}b+\frac{2}{5}q+\frac{7}{25} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-9}{12}-x)(q-\frac{8}{11})& =(\color{red}{-x}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{8}{11}x-\frac{3}{4}q+\frac{3}{4}.\frac{8}{11}& \text{Uitwerken } \\ & =-qx+\frac{8}{11}x-\frac{3}{4}q+\frac{24}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{8}{11}x-\frac{3}{4}q+\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{-13}{13})(\frac{14}{10}+q)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{5}x-1q-1.\frac{7}{5}& \text{Uitwerken } \\ & =qx+\frac{7}{5}x-1q-\frac{7}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-17}{4})(\frac{-6}{6}-x)& =(\color{red}{x}+\color{orange}{\frac{-17}{4}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -xx-1x+\frac{17}{4}x+\frac{17}{4}.1& \text{Uitwerken } \\ & =-x^2+((-1)+\frac{17}{4})x+(\frac{-17}{4}) & \text{Neem samen} \\ &=-x^2+\frac{13}{4}x+(\frac{-17}{4}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}((-18)-x)(a+\frac{20}{6})& =(\color{red}{-x}+\color{orange}{(-18)}).(\color{green}{a}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(-18)} . \color{green}{(a)} + \color{orange}{(-18)} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{10}{3}x-18a-18.\frac{10}{3}& \text{Uitwerken } \\ & =-ax-\frac{10}{3}x-18a-\frac{180}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{10}{3}x-18a-60 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{12}{19}+x)(a-\frac{-19}{4})& =(\color{red}{x}+\color{orange}{\frac{12}{19}}).(\color{green}{a}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{12}{19})} . \color{green}{(a)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{4}x+\frac{12}{19}a+\frac{12}{19}.\frac{19}{4}& \text{Uitwerken } \\ & =ax+\frac{19}{4}x+\frac{12}{19}a+\frac{228}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{19}{4}x+\frac{12}{19}a+3 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(b-\frac{18}{19})(\frac{-3}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{4}b-\frac{18}{19}q+\frac{18}{19}.\frac{1}{4}& \text{Uitwerken } \\ & =bq-\frac{1}{4}b-\frac{18}{19}q+\frac{18}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{4}b-\frac{18}{19}q+\frac{9}{38} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{2}{10}-a)(\frac{20}{9}+q)& =(\color{red}{-a}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{20}{9}a+\frac{1}{5}q+\frac{1}{5}.\frac{20}{9}& \text{Uitwerken } \\ & =-aq-\frac{20}{9}a+\frac{1}{5}q+\frac{20}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{20}{9}a+\frac{1}{5}q+\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x-\frac{4}{2})(q-\frac{11}{11})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-2q+2.1& \text{Uitwerken } \\ & =qx-1x-2q+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{-10}{19})(p-\frac{11}{7})& =(\color{red}{q}+\color{orange}{\frac{-10}{19}}).(\color{green}{p}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{7}q-\frac{10}{19}p+\frac{10}{19}.\frac{11}{7}& \text{Uitwerken } \\ & =pq-\frac{11}{7}q-\frac{10}{19}p+\frac{110}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)