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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{-15}{16})(\frac{17}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{-15}{16}}).(\color{green}{b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{5}q-\frac{15}{16}b-\frac{15}{16}.\frac{17}{5}& \text{Uitwerken } \\ & =bq+\frac{17}{5}q-\frac{15}{16}b-\frac{255}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{5}q-\frac{15}{16}b-\frac{51}{16} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(q+\frac{3}{3})((-3)+p)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pq-3q+1p-1.3& \text{Uitwerken } \\ & =pq-3q+1p-3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{7}+p)(\frac{11}{14}-x)& =(\color{red}{p}+\color{orange}{\frac{-1}{7}}).(\color{green}{-x}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{11}{14}p+\frac{1}{7}x-\frac{1}{7}.\frac{11}{14}& \text{Uitwerken } \\ & =-px+\frac{11}{14}p+\frac{1}{7}x-\frac{11}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-5}{14})(\frac{-11}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{5}{14}}).(\color{green}{-a}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{5}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{11}{6}q-\frac{5}{14}a-\frac{5}{14}.\frac{11}{6}& \text{Uitwerken } \\ & =-aq-\frac{11}{6}q-\frac{5}{14}a-\frac{55}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{11}{17}+x)(\frac{-6}{10}-p)& =(\color{red}{x}+\color{orange}{\frac{11}{17}}).(\color{green}{-p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{11}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{5}x-\frac{11}{17}p-\frac{11}{17}.\frac{3}{5}& \text{Uitwerken } \\ & =-px-\frac{3}{5}x-\frac{11}{17}p-\frac{33}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-18}{2}-p)(x-\frac{-12}{15})& =(\color{red}{-p}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{5}p-9x-9.\frac{4}{5}& \text{Uitwerken } \\ & =-px-\frac{4}{5}p-9x-\frac{36}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{20}{3})(b-\frac{-14}{15})& =(\color{red}{p}+\color{orange}{\frac{-20}{3}}).(\color{green}{b}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{14}{15}p-\frac{20}{3}b-\frac{20}{3}.\frac{14}{15}& \text{Uitwerken } \\ & =bp+\frac{14}{15}p-\frac{20}{3}b-\frac{280}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{14}{15}p-\frac{20}{3}b-\frac{56}{9} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{17}{12}+p)(x+\frac{-2}{17})& =(\color{red}{p}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{17}p+\frac{17}{12}x-\frac{17}{12}.\frac{2}{17}& \text{Uitwerken } \\ & =px-\frac{2}{17}p+\frac{17}{12}x-\frac{34}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{17}p+\frac{17}{12}x-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-4}{5}-a)(x-18)& =(\color{red}{-a}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{(-18)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-18)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -ax+18a-\frac{4}{5}x+\frac{4}{5}.18& \text{Uitwerken } \\ & =-ax+18a-\frac{4}{5}x+\frac{72}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{-20}{8})(\frac{5}{13}-b)& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{-b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{13}x+\frac{5}{2}b-\frac{5}{2}.\frac{5}{13}& \text{Uitwerken } \\ & =-bx+\frac{5}{13}x+\frac{5}{2}b-\frac{25}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{3}{20})(\frac{-14}{9}-b)& =(\color{red}{a}+\color{orange}{\frac{-3}{20}}).(\color{green}{-b}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{14}{9}a+\frac{3}{20}b+\frac{3}{20}.\frac{14}{9}& \text{Uitwerken } \\ & =-ab-\frac{14}{9}a+\frac{3}{20}b+\frac{42}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{14}{9}a+\frac{3}{20}b+\frac{7}{30} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a-\frac{-2}{19})(\frac{12}{10}+x)& =(\color{red}{a}+\color{orange}{\frac{2}{19}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{2}{19})} . \color{green}{(x)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{5}a+\frac{2}{19}x+\frac{2}{19}.\frac{6}{5}& \text{Uitwerken } \\ & =ax+\frac{6}{5}a+\frac{2}{19}x+\frac{12}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)