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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+11)(a+\frac{-11}{7})& =(\color{red}{q}+\color{orange}{11}).(\color{green}{a}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(11)} . \color{green}{(a)} + \color{orange}{(11)} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{7}q+11a-11.\frac{11}{7}& \text{Uitwerken } \\ & =aq-\frac{11}{7}q+11a-\frac{121}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{13}{16}+a)(\frac{3}{14}+b)& =(\color{red}{a}+\color{orange}{\frac{13}{16}}).(\color{green}{b}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{14}a+\frac{13}{16}b+\frac{13}{16}.\frac{3}{14}& \text{Uitwerken } \\ & =ab+\frac{3}{14}a+\frac{13}{16}b+\frac{39}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{13}{16})(\frac{-2}{14}-x)& =(\color{red}{b}+\color{orange}{\frac{13}{16}}).(\color{green}{-x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{13}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{7}b-\frac{13}{16}x-\frac{13}{16}.\frac{1}{7}& \text{Uitwerken } \\ & =-bx-\frac{1}{7}b-\frac{13}{16}x-\frac{13}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{19}{12}-q)(b-\frac{-12}{8})& =(\color{red}{-q}+\color{orange}{\frac{19}{12}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{19}{12})} . \color{green}{(b)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{2}q+\frac{19}{12}b+\frac{19}{12}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq-\frac{3}{2}q+\frac{19}{12}b+\frac{57}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{3}{2}q+\frac{19}{12}b+\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a+\frac{5}{5})(a+\frac{-12}{15})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{5}a+1a-1.\frac{4}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{5})+1)a-(\frac{-4}{5}) & \text{Neem samen} \\ &=a^2+\frac{1}{5}a-(\frac{-4}{5}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{7}{4}-p)(q-\frac{11}{17})& =(\color{red}{-p}+\color{orange}{\frac{7}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{17}p+\frac{7}{4}q-\frac{7}{4}.\frac{11}{17}& \text{Uitwerken } \\ & =-pq+\frac{11}{17}p+\frac{7}{4}q-\frac{77}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-2}{11}-p)(b-13)& =(\color{red}{-p}+\color{orange}{\frac{-2}{11}}).(\color{green}{b}+\color{blue}{(-13)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-13)} + \color{orange}{(\frac{-2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -bp+13p-\frac{2}{11}b+\frac{2}{11}.13& \text{Uitwerken } \\ & =-bp+13p-\frac{2}{11}b+\frac{26}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{20}{2}-x)(\frac{6}{4}-b)& =(\color{red}{-x}+\color{orange}{10}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(10)} . \color{green}{(-b)} + \color{orange}{(10)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{2}x-10b+10.\frac{3}{2}& \text{Uitwerken } \\ & =bx-\frac{3}{2}x-10b+\frac{30}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{2}x-10b+15 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p-\frac{-5}{5})(\frac{-11}{11}-b)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1p-1b-1.1& \text{Uitwerken } \\ & =-bp-1p-1b-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{-3}{6})(\frac{9}{8}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{8}q+\frac{1}{2}a+\frac{1}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =aq+\frac{9}{8}q+\frac{1}{2}a+\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-4}{7}-q)(\frac{-5}{8}+q)& =(\color{red}{-q}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{5}{8}q-\frac{4}{7}q+\frac{4}{7}.\frac{5}{8}& \text{Uitwerken } \\ & =-q^2+(\frac{5}{8}+(\frac{-4}{7}))q+(\frac{-20}{56}) & \text{Neem samen} \\ &=-q^2+\frac{3}{56}q+(\frac{-20}{56}) & \text{Maak de som} \\ &=-q^2+\frac{3}{56}q+(\frac{-5}{14}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(q+\frac{11}{15})(b-\frac{6}{14})& =(\color{red}{q}+\color{orange}{\frac{11}{15}}).(\color{green}{b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{7}q+\frac{11}{15}b-\frac{11}{15}.\frac{3}{7}& \text{Uitwerken } \\ & =bq-\frac{3}{7}q+\frac{11}{15}b-\frac{33}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{7}q+\frac{11}{15}b-\frac{11}{35} & \text{Vereenvoudig} \\\end{align}\)