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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{1}{14})(x-\frac{19}{19})& =(\color{red}{x}+\color{orange}{\frac{1}{14}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{14})} . \color{green}{(x)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x+\frac{1}{14}x-\frac{1}{14}.1& \text{Uitwerken } \\ & =x^2+((-1)+\frac{1}{14})x-(\frac{-1}{14}) & \text{Neem samen} \\ &=x^2-\frac{13}{14}x-(\frac{-1}{14}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{15}+q)(\frac{7}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{20}q-\frac{3}{5}a-\frac{3}{5}.\frac{7}{20}& \text{Uitwerken } \\ & =aq+\frac{7}{20}q-\frac{3}{5}a-\frac{21}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{10}{19})(\frac{-3}{9}-b)& =(\color{red}{b}+\color{orange}{\frac{10}{19}}).(\color{green}{-b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{10}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{3}b-\frac{10}{19}b-\frac{10}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{3})+(\frac{-10}{19}))b-\frac{10}{57} & \text{Neem samen} \\ &=-b^2-\frac{49}{57}b-\frac{10}{57} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{11}{4}+a)(\frac{3}{20}-q)& =(\color{red}{a}+\color{orange}{\frac{11}{4}}).(\color{green}{-q}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{11}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{20}a-\frac{11}{4}q+\frac{11}{4}.\frac{3}{20}& \text{Uitwerken } \\ & =-aq+\frac{3}{20}a-\frac{11}{4}q+\frac{33}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{14}{6})(\frac{8}{14}+q)& =(\color{red}{x}+\color{orange}{\frac{7}{3}}).(\color{green}{q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{7}x+\frac{7}{3}q+\frac{7}{3}.\frac{4}{7}& \text{Uitwerken } \\ & =qx+\frac{4}{7}x+\frac{7}{3}q+\frac{28}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{7}x+\frac{7}{3}q+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{-1}{7})(q-\frac{-2}{6})& =(\color{red}{b}+\color{orange}{\frac{-1}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}b-\frac{1}{7}q-\frac{1}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}b-\frac{1}{7}q-\frac{1}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{-3}{3})(q-\frac{-11}{13})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{13}x-1q-1.\frac{11}{13}& \text{Uitwerken } \\ & =qx+\frac{11}{13}x-1q-\frac{11}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-12}{16}-q)(p+\frac{-6}{14})& =(\color{red}{-q}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{7}q-\frac{3}{4}p+\frac{3}{4}.\frac{3}{7}& \text{Uitwerken } \\ & =-pq+\frac{3}{7}q-\frac{3}{4}p+\frac{9}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{11}{2})(\frac{20}{5}-p)& =(\color{red}{a}+\color{orange}{\frac{-11}{2}}).(\color{green}{-p}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{-11}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -ap+4a+\frac{11}{2}p-\frac{11}{2}.4& \text{Uitwerken } \\ & =-ap+4a+\frac{11}{2}p-\frac{44}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+4a+\frac{11}{2}p-22 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a+\frac{-11}{7})(\frac{-9}{19}+x)& =(\color{red}{a}+\color{orange}{\frac{-11}{7}}).(\color{green}{x}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{19}a-\frac{11}{7}x+\frac{11}{7}.\frac{9}{19}& \text{Uitwerken } \\ & =ax-\frac{9}{19}a-\frac{11}{7}x+\frac{99}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-12}{8}-b)(a+\frac{16}{12})& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{3}b-\frac{3}{2}a-\frac{3}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =-ab-\frac{4}{3}b-\frac{3}{2}a-\frac{12}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{4}{3}b-\frac{3}{2}a-2 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(b-\frac{10}{9})(a+\frac{-8}{3})& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{3}b-\frac{10}{9}a+\frac{10}{9}.\frac{8}{3}& \text{Uitwerken } \\ & =ab-\frac{8}{3}b-\frac{10}{9}a+\frac{80}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)