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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{1}{7})(\frac{-4}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{1}{7}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{5}q+\frac{1}{7}b-\frac{1}{7}.\frac{4}{5}& \text{Uitwerken } \\ & =bq-\frac{4}{5}q+\frac{1}{7}b-\frac{4}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{-4}{9})(\frac{18}{3}+a)& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ax+6x+\frac{4}{9}a+\frac{4}{9}.6& \text{Uitwerken } \\ & =ax+6x+\frac{4}{9}a+\frac{24}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+6x+\frac{4}{9}a+\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-20}{10}-a)(\frac{-8}{3}-a)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{-a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(-2)} . \color{green}{(-a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{8}{3}a+2a+2.\frac{8}{3}& \text{Uitwerken } \\ & =a^2+(\frac{8}{3}+2)a+\frac{16}{3} & \text{Neem samen} \\ &=a^2+\frac{14}{3}a+\frac{16}{3} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(x+\frac{-2}{3})(\frac{4}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{-b}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{15}x+\frac{2}{3}b-\frac{2}{3}.\frac{4}{15}& \text{Uitwerken } \\ & =-bx+\frac{4}{15}x+\frac{2}{3}b-\frac{8}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-5}{14}+q)(\frac{3}{7}-p)& =(\color{red}{q}+\color{orange}{\frac{-5}{14}}).(\color{green}{-p}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{7}q+\frac{5}{14}p-\frac{5}{14}.\frac{3}{7}& \text{Uitwerken } \\ & =-pq+\frac{3}{7}q+\frac{5}{14}p-\frac{15}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{-4}{19})(p-\frac{11}{6})& =(\color{red}{q}+\color{orange}{\frac{-4}{19}}).(\color{green}{p}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{6}q-\frac{4}{19}p+\frac{4}{19}.\frac{11}{6}& \text{Uitwerken } \\ & =pq-\frac{11}{6}q-\frac{4}{19}p+\frac{44}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{11}{6}q-\frac{4}{19}p+\frac{22}{57} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{12}{7})(b+\frac{1}{18})& =(\color{red}{b}+\color{orange}{\frac{-12}{7}}).(\color{green}{b}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-12}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{18}b-\frac{12}{7}b-\frac{12}{7}.\frac{1}{18}& \text{Uitwerken } \\ & =b^2+(\frac{1}{18}+(\frac{-12}{7}))b-(\frac{-12}{126}) & \text{Neem samen} \\ &=b^2-\frac{209}{126}b-(\frac{-12}{126}) & \text{Maak de som} \\ &=b^2-\frac{209}{126}b+\frac{2}{21} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(q-\frac{-1}{20})(\frac{9}{3}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{20}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{20})} . \color{green}{(x)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qx+3q+\frac{1}{20}x+\frac{1}{20}.3& \text{Uitwerken } \\ & =qx+3q+\frac{1}{20}x+\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(9-a)(b-\frac{-6}{11})& =(\color{red}{-a}+\color{orange}{9}).(\color{green}{b}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(9)} . \color{green}{(b)} + \color{orange}{(9)} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{6}{11}a+9b+9.\frac{6}{11}& \text{Uitwerken } \\ & =-ab-\frac{6}{11}a+9b+\frac{54}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-12}{14}-q)(\frac{-5}{12}-x)& =(\color{red}{-q}+\color{orange}{\frac{-6}{7}}).(\color{green}{-x}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{12}q+\frac{6}{7}x+\frac{6}{7}.\frac{5}{12}& \text{Uitwerken } \\ & =qx+\frac{5}{12}q+\frac{6}{7}x+\frac{30}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{12}q+\frac{6}{7}x+\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a+\frac{4}{5})(\frac{-14}{10}+q)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{q}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{5}a+\frac{4}{5}q-\frac{4}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =aq-\frac{7}{5}a+\frac{4}{5}q-\frac{28}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{7}{8}+q)(\frac{-9}{8}-a)& =(\color{red}{q}+\color{orange}{\frac{7}{8}}).(\color{green}{-a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{7}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{8}q-\frac{7}{8}a-\frac{7}{8}.\frac{9}{8}& \text{Uitwerken } \\ & =-aq-\frac{9}{8}q-\frac{7}{8}a-\frac{63}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)