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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{13}-b)(x-\frac{-3}{19})& =(\color{red}{-b}+\color{orange}{\frac{-10}{13}}).(\color{green}{x}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{19}b-\frac{10}{13}x-\frac{10}{13}.\frac{3}{19}& \text{Uitwerken } \\ & =-bx-\frac{3}{19}b-\frac{10}{13}x-\frac{30}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{-12}{17})(x+\frac{-20}{17})& =(\color{red}{x}+\color{orange}{\frac{12}{17}}).(\color{green}{x}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{12}{17})} . \color{green}{(x)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{20}{17}x+\frac{12}{17}x-\frac{12}{17}.\frac{20}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-20}{17})+\frac{12}{17})x-(\frac{-240}{289}) & \text{Neem samen} \\ &=x^2-\frac{8}{17}x-(\frac{-240}{289}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(x-\frac{-16}{11})(p-\frac{10}{13})& =(\color{red}{x}+\color{orange}{\frac{16}{11}}).(\color{green}{p}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{16}{11})} . \color{green}{(p)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{13}x+\frac{16}{11}p-\frac{16}{11}.\frac{10}{13}& \text{Uitwerken } \\ & =px-\frac{10}{13}x+\frac{16}{11}p-\frac{160}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{14}{12}-a)(p-\frac{7}{3})& =(\color{red}{-a}+\color{orange}{\frac{7}{6}}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{3}a+\frac{7}{6}p-\frac{7}{6}.\frac{7}{3}& \text{Uitwerken } \\ & =-ap+\frac{7}{3}a+\frac{7}{6}p-\frac{49}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{4}{4}+a)(\frac{8}{7}-q)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{8}{7}a-1q+1.\frac{8}{7}& \text{Uitwerken } \\ & =-aq+\frac{8}{7}a-1q+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{10}{16}+b)(q-\frac{15}{8})& =(\color{red}{b}+\color{orange}{\frac{5}{8}}).(\color{green}{q}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{5}{8})} . \color{green}{(q)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{8}b+\frac{5}{8}q-\frac{5}{8}.\frac{15}{8}& \text{Uitwerken } \\ & =bq-\frac{15}{8}b+\frac{5}{8}q-\frac{75}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{12}{8})(p+\frac{-20}{14})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{7}q+\frac{3}{2}p-\frac{3}{2}.\frac{10}{7}& \text{Uitwerken } \\ & =pq-\frac{10}{7}q+\frac{3}{2}p-\frac{30}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{10}{7}q+\frac{3}{2}p-\frac{15}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{-8}{20})(\frac{4}{10}+b)& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{5}q+\frac{2}{5}b+\frac{2}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =bq+\frac{2}{5}q+\frac{2}{5}b+\frac{4}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{-11}{18})(q-\frac{4}{4})& =(\color{red}{b}+\color{orange}{\frac{11}{18}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{18})} . \color{green}{(q)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b+\frac{11}{18}q-\frac{11}{18}.1& \text{Uitwerken } \\ & =bq-1b+\frac{11}{18}q-\frac{11}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-1}{8}+p)(q-\frac{-11}{15})& =(\color{red}{p}+\color{orange}{\frac{-1}{8}}).(\color{green}{q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{15}p-\frac{1}{8}q-\frac{1}{8}.\frac{11}{15}& \text{Uitwerken } \\ & =pq+\frac{11}{15}p-\frac{1}{8}q-\frac{11}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{-17}{14})(\frac{2}{6}+p)& =(\color{red}{b}+\color{orange}{\frac{17}{14}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{17}{14})} . \color{green}{(p)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{3}b+\frac{17}{14}p+\frac{17}{14}.\frac{1}{3}& \text{Uitwerken } \\ & =bp+\frac{1}{3}b+\frac{17}{14}p+\frac{17}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(9+p)(q+\frac{7}{2})& =(\color{red}{p}+\color{orange}{9}).(\color{green}{q}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(9)} . \color{green}{(q)} + \color{orange}{(9)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{2}p+9q+9.\frac{7}{2}& \text{Uitwerken } \\ & =pq+\frac{7}{2}p+9q+\frac{63}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)