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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{6}+b)(\frac{16}{2}+x)& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{8})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(8)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = bx+8b-\frac{5}{2}x-\frac{5}{2}.8& \text{Uitwerken } \\ & =bx+8b-\frac{5}{2}x-\frac{40}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+8b-\frac{5}{2}x-20 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-7}{15}-q)(x+\frac{-15}{12})& =(\color{red}{-q}+\color{orange}{\frac{-7}{15}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{4}q-\frac{7}{15}x+\frac{7}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =-qx+\frac{5}{4}q-\frac{7}{15}x+\frac{35}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{5}{4}q-\frac{7}{15}x+\frac{7}{12} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a+\frac{-11}{13})(\frac{14}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{-11}{13}}).(\color{green}{-x}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{14}{15}a+\frac{11}{13}x-\frac{11}{13}.\frac{14}{15}& \text{Uitwerken } \\ & =-ax+\frac{14}{15}a+\frac{11}{13}x-\frac{154}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-17}{13}+p)(x-\frac{15}{9})& =(\color{red}{p}+\color{orange}{\frac{-17}{13}}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{3}p-\frac{17}{13}x+\frac{17}{13}.\frac{5}{3}& \text{Uitwerken } \\ & =px-\frac{5}{3}p-\frac{17}{13}x+\frac{85}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-11}{3}-p)(\frac{-17}{20}-q)& =(\color{red}{-p}+\color{orange}{\frac{-11}{3}}).(\color{green}{-q}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{20}p+\frac{11}{3}q+\frac{11}{3}.\frac{17}{20}& \text{Uitwerken } \\ & =pq+\frac{17}{20}p+\frac{11}{3}q+\frac{187}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{16}{18}+a)(b-\frac{-18}{13})& =(\color{red}{a}+\color{orange}{\frac{8}{9}}).(\color{green}{b}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{18}{13}a+\frac{8}{9}b+\frac{8}{9}.\frac{18}{13}& \text{Uitwerken } \\ & =ab+\frac{18}{13}a+\frac{8}{9}b+\frac{144}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{18}{13}a+\frac{8}{9}b+\frac{16}{13} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{14}{8}+p)(q+\frac{-4}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{4}}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{5}p+\frac{7}{4}q-\frac{7}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =pq-\frac{4}{5}p+\frac{7}{4}q-\frac{28}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{5}p+\frac{7}{4}q-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p+\frac{8}{11})(x+\frac{3}{14})& =(\color{red}{p}+\color{orange}{\frac{8}{11}}).(\color{green}{x}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{8}{11})} . \color{green}{(x)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{14}p+\frac{8}{11}x+\frac{8}{11}.\frac{3}{14}& \text{Uitwerken } \\ & =px+\frac{3}{14}p+\frac{8}{11}x+\frac{24}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{14}p+\frac{8}{11}x+\frac{12}{77} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{10}{10}-p)(\frac{-9}{7}+q)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{7}p+1q-1.\frac{9}{7}& \text{Uitwerken } \\ & =-pq+\frac{9}{7}p+1q-\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{15}{14}-a)(p+\frac{15}{10})& =(\color{red}{-a}+\color{orange}{\frac{15}{14}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{15}{14})} . \color{green}{(p)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{2}a+\frac{15}{14}p+\frac{15}{14}.\frac{3}{2}& \text{Uitwerken } \\ & =-ap-\frac{3}{2}a+\frac{15}{14}p+\frac{45}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-18}{9})(p-\frac{7}{9})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{9}a+2p-2.\frac{7}{9}& \text{Uitwerken } \\ & =ap-\frac{7}{9}a+2p-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{14}{9})(\frac{-2}{20}+x)& =(\color{red}{b}+\color{orange}{\frac{-14}{9}}).(\color{green}{x}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{10}b-\frac{14}{9}x+\frac{14}{9}.\frac{1}{10}& \text{Uitwerken } \\ & =bx-\frac{1}{10}b-\frac{14}{9}x+\frac{14}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{10}b-\frac{14}{9}x+\frac{7}{45} & \text{Vereenvoudig} \\\end{align}\)