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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-17}{9})(x-\frac{3}{6})& =(\color{red}{a}+\color{orange}{\frac{17}{9}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{17}{9})} . \color{green}{(x)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a+\frac{17}{9}x-\frac{17}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a+\frac{17}{9}x-\frac{17}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{13}{5})(p-\frac{5}{15})& =(\color{red}{b}+\color{orange}{\frac{-13}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{3}b-\frac{13}{5}p+\frac{13}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =bp-\frac{1}{3}b-\frac{13}{5}p+\frac{13}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-2}{16})(\frac{6}{5}+p)& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{6}{5}x+\frac{1}{8}p+\frac{1}{8}.\frac{6}{5}& \text{Uitwerken } \\ & =px+\frac{6}{5}x+\frac{1}{8}p+\frac{6}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{6}{5}x+\frac{1}{8}p+\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x-\frac{-3}{2})(\frac{4}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{19}x+\frac{3}{2}a+\frac{3}{2}.\frac{4}{19}& \text{Uitwerken } \\ & =ax+\frac{4}{19}x+\frac{3}{2}a+\frac{12}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{4}{19}x+\frac{3}{2}a+\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b+\frac{15}{6})(\frac{-7}{10}+p)& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{10}b+\frac{5}{2}p-\frac{5}{2}.\frac{7}{10}& \text{Uitwerken } \\ & =bp-\frac{7}{10}b+\frac{5}{2}p-\frac{35}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{10}b+\frac{5}{2}p-\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x+\frac{10}{12})(p-\frac{-4}{20})& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{5}x+\frac{5}{6}p+\frac{5}{6}.\frac{1}{5}& \text{Uitwerken } \\ & =px+\frac{1}{5}x+\frac{5}{6}p+\frac{5}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{5}x+\frac{5}{6}p+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{12}{19}+q)(b+\frac{12}{20})& =(\color{red}{q}+\color{orange}{\frac{12}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{12}{19})} . \color{green}{(b)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{5}q+\frac{12}{19}b+\frac{12}{19}.\frac{3}{5}& \text{Uitwerken } \\ & =bq+\frac{3}{5}q+\frac{12}{19}b+\frac{36}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-11}{15}+a)(\frac{-6}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{-11}{15}}).(\color{green}{-x}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{6}{11}a+\frac{11}{15}x+\frac{11}{15}.\frac{6}{11}& \text{Uitwerken } \\ & =-ax-\frac{6}{11}a+\frac{11}{15}x+\frac{66}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{6}{11}a+\frac{11}{15}x+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{-4}{8})(a-\frac{-10}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{7}q+\frac{1}{2}a+\frac{1}{2}.\frac{10}{7}& \text{Uitwerken } \\ & =aq+\frac{10}{7}q+\frac{1}{2}a+\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{7}q+\frac{1}{2}a+\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{2}{15})(x-\frac{11}{5})& =(\color{red}{q}+\color{orange}{\frac{2}{15}}).(\color{green}{x}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{2}{15})} . \color{green}{(x)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{5}q+\frac{2}{15}x-\frac{2}{15}.\frac{11}{5}& \text{Uitwerken } \\ & =qx-\frac{11}{5}q+\frac{2}{15}x-\frac{22}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{-2}{16})(p-\frac{-9}{10})& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{p}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{10}p+\frac{1}{8}p+\frac{1}{8}.\frac{9}{10}& \text{Uitwerken } \\ & =p^2+(\frac{9}{10}+\frac{1}{8})p+\frac{9}{80} & \text{Neem samen} \\ &=p^2+\frac{41}{40}p+\frac{9}{80} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{18}{15}+a)(10-b)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-b}+\color{blue}{10})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(10)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -ab+10a-\frac{6}{5}b+\frac{6}{5}.10& \text{Uitwerken } \\ & =-ab+10a-\frac{6}{5}b+\frac{60}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+10a-\frac{6}{5}b+12 & \text{Vereenvoudig} \\\end{align}\)