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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{1}{13}-b)(q+\frac{2}{11})& =(\color{red}{-b}+\color{orange}{\frac{1}{13}}).(\color{green}{q}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{1}{13})} . \color{green}{(q)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{11}b+\frac{1}{13}q+\frac{1}{13}.\frac{2}{11}& \text{Uitwerken } \\ & =-bq-\frac{2}{11}b+\frac{1}{13}q+\frac{2}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{18}{3})(\frac{-8}{2}+x)& =(\color{red}{a}+\color{orange}{6}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(6)} . \color{green}{(x)} + \color{orange}{(6)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ax-4a+6x-6.4& \text{Uitwerken } \\ & =ax-4a+6x-24 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{12}{9}+p)(\frac{13}{20}+q)& =(\color{red}{p}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{13}{20}p+\frac{4}{3}q+\frac{4}{3}.\frac{13}{20}& \text{Uitwerken } \\ & =pq+\frac{13}{20}p+\frac{4}{3}q+\frac{52}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{13}{20}p+\frac{4}{3}q+\frac{13}{15} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(13-p)(a-\frac{4}{15})& =(\color{red}{-p}+\color{orange}{13}).(\color{green}{a}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(13)} . \color{green}{(a)} + \color{orange}{(13)} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{15}p+13a-13.\frac{4}{15}& \text{Uitwerken } \\ & =-ap+\frac{4}{15}p+13a-\frac{52}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{8}-x)(\frac{12}{14}-a)& =(\color{red}{-x}+\color{orange}{\frac{9}{4}}).(\color{green}{-a}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{6}{7}x-\frac{9}{4}a+\frac{9}{4}.\frac{6}{7}& \text{Uitwerken } \\ & =ax-\frac{6}{7}x-\frac{9}{4}a+\frac{54}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{6}{7}x-\frac{9}{4}a+\frac{27}{14} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{14}{7}-a)(a+\frac{-20}{13})& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{20}{13}a+2a-2.\frac{20}{13}& \text{Uitwerken } \\ & =-a^2+(\frac{20}{13}+2)a-\frac{40}{13} & \text{Neem samen} \\ &=-a^2+\frac{46}{13}a-\frac{40}{13} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(q-\frac{-1}{9})(\frac{-1}{20}+p)& =(\color{red}{q}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{20}q+\frac{1}{9}p-\frac{1}{9}.\frac{1}{20}& \text{Uitwerken } \\ & =pq-\frac{1}{20}q+\frac{1}{9}p-\frac{1}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-15}{2}+p)(x+\frac{-13}{13})& =(\color{red}{p}+\color{orange}{\frac{-15}{2}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-15}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p-\frac{15}{2}x+\frac{15}{2}.1& \text{Uitwerken } \\ & =px-1p-\frac{15}{2}x+\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-20}{19}+a)(\frac{-15}{15}+a)& =(\color{red}{a}+\color{orange}{\frac{-20}{19}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-20}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aa-1a-\frac{20}{19}a+\frac{20}{19}.1& \text{Uitwerken } \\ & =a^2+((-1)+(\frac{-20}{19}))a+\frac{20}{19} & \text{Neem samen} \\ &=a^2-\frac{39}{19}a+\frac{20}{19} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(b-\frac{6}{20})(p+\frac{15}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{6}b-\frac{3}{10}p-\frac{3}{10}.\frac{5}{6}& \text{Uitwerken } \\ & =bp+\frac{5}{6}b-\frac{3}{10}p-\frac{15}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{6}b-\frac{3}{10}p-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{-5}{18})(b-\frac{10}{9})& =(\color{red}{p}+\color{orange}{\frac{-5}{18}}).(\color{green}{b}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{10}{9}p-\frac{5}{18}b+\frac{5}{18}.\frac{10}{9}& \text{Uitwerken } \\ & =bp-\frac{10}{9}p-\frac{5}{18}b+\frac{50}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{10}{9}p-\frac{5}{18}b+\frac{25}{81} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-2}{15}+a)(\frac{-20}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-2}{15}}).(\color{green}{q}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{20}{17}a-\frac{2}{15}q+\frac{2}{15}.\frac{20}{17}& \text{Uitwerken } \\ & =aq-\frac{20}{17}a-\frac{2}{15}q+\frac{40}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{20}{17}a-\frac{2}{15}q+\frac{8}{51} & \text{Vereenvoudig} \\\end{align}\)