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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{11}{3})(q+\frac{9}{4})& =(\color{red}{b}+\color{orange}{\frac{11}{3}}).(\color{green}{q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{11}{3})} . \color{green}{(q)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{4}b+\frac{11}{3}q+\frac{11}{3}.\frac{9}{4}& \text{Uitwerken } \\ & =bq+\frac{9}{4}b+\frac{11}{3}q+\frac{99}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{9}{4}b+\frac{11}{3}q+\frac{33}{4} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{-13}{17})(x+\frac{16}{15})& =(\color{red}{p}+\color{orange}{\frac{13}{17}}).(\color{green}{x}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{16}{15}p+\frac{13}{17}x+\frac{13}{17}.\frac{16}{15}& \text{Uitwerken } \\ & =px+\frac{16}{15}p+\frac{13}{17}x+\frac{208}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-13}{16})(\frac{-1}{8}-a)& =(\color{red}{p}+\color{orange}{\frac{-13}{16}}).(\color{green}{-a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{8}p+\frac{13}{16}a+\frac{13}{16}.\frac{1}{8}& \text{Uitwerken } \\ & =-ap-\frac{1}{8}p+\frac{13}{16}a+\frac{13}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{7}{6})(\frac{-15}{10}-q)& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{-q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{2}a+\frac{7}{6}q+\frac{7}{6}.\frac{3}{2}& \text{Uitwerken } \\ & =-aq-\frac{3}{2}a+\frac{7}{6}q+\frac{21}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{3}{2}a+\frac{7}{6}q+\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{18}{10}+b)(q+\frac{-4}{18})& =(\color{red}{b}+\color{orange}{\frac{9}{5}}).(\color{green}{q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{9}b+\frac{9}{5}q-\frac{9}{5}.\frac{2}{9}& \text{Uitwerken } \\ & =bq-\frac{2}{9}b+\frac{9}{5}q-\frac{18}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{2}{9}b+\frac{9}{5}q-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p-\frac{-20}{13})(\frac{-17}{19}-x)& =(\color{red}{p}+\color{orange}{\frac{20}{13}}).(\color{green}{-x}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{20}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{19}p-\frac{20}{13}x-\frac{20}{13}.\frac{17}{19}& \text{Uitwerken } \\ & =-px-\frac{17}{19}p-\frac{20}{13}x-\frac{340}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x-\frac{12}{10})(q+\frac{-2}{6})& =(\color{red}{x}+\color{orange}{\frac{-6}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{3}x-\frac{6}{5}q+\frac{6}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =qx-\frac{1}{3}x-\frac{6}{5}q+\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{3}x-\frac{6}{5}q+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x+\frac{-20}{14})(p-\frac{4}{15})& =(\color{red}{x}+\color{orange}{\frac{-10}{7}}).(\color{green}{p}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{15}x-\frac{10}{7}p+\frac{10}{7}.\frac{4}{15}& \text{Uitwerken } \\ & =px-\frac{4}{15}x-\frac{10}{7}p+\frac{40}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{15}x-\frac{10}{7}p+\frac{8}{21} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{7}{19}+b)(a+\frac{13}{11})& =(\color{red}{b}+\color{orange}{\frac{7}{19}}).(\color{green}{a}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{7}{19})} . \color{green}{(a)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{11}b+\frac{7}{19}a+\frac{7}{19}.\frac{13}{11}& \text{Uitwerken } \\ & =ab+\frac{13}{11}b+\frac{7}{19}a+\frac{91}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{3}{13}-p)(\frac{14}{17}-p)& =(\color{red}{-p}+\color{orange}{\frac{3}{13}}).(\color{green}{-p}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{3}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{14}{17}p-\frac{3}{13}p+\frac{3}{13}.\frac{14}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-14}{17})+(\frac{-3}{13}))p+\frac{42}{221} & \text{Neem samen} \\ &=p^2-\frac{233}{221}p+\frac{42}{221} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(b+\frac{-6}{7})(\frac{7}{19}+q)& =(\color{red}{b}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{19}b-\frac{6}{7}q-\frac{6}{7}.\frac{7}{19}& \text{Uitwerken } \\ & =bq+\frac{7}{19}b-\frac{6}{7}q-\frac{42}{133} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{19}b-\frac{6}{7}q-\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x-\frac{-1}{4})(\frac{19}{19}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x-\frac{1}{4}b+\frac{1}{4}.1& \text{Uitwerken } \\ & =-bx+1x-\frac{1}{4}b+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)