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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{20}+b)(p-\frac{14}{19})& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{19}b+\frac{4}{5}p-\frac{4}{5}.\frac{14}{19}& \text{Uitwerken } \\ & =bp-\frac{14}{19}b+\frac{4}{5}p-\frac{56}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-5}{9}+b)(b+\frac{-5}{19})& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{b}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{19}b-\frac{5}{9}b+\frac{5}{9}.\frac{5}{19}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{19})+(\frac{-5}{9}))b+\frac{25}{171} & \text{Neem samen} \\ &=b^2-\frac{140}{171}b+\frac{25}{171} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(b+\frac{16}{4})(q-\frac{-7}{14})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{2}b+4q+4.\frac{1}{2}& \text{Uitwerken } \\ & =bq+\frac{1}{2}b+4q+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{2}b+4q+2 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b-\frac{-6}{13})(q-\frac{-7}{19})& =(\color{red}{b}+\color{orange}{\frac{6}{13}}).(\color{green}{q}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{19}b+\frac{6}{13}q+\frac{6}{13}.\frac{7}{19}& \text{Uitwerken } \\ & =bq+\frac{7}{19}b+\frac{6}{13}q+\frac{42}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p-\frac{-17}{14})(\frac{13}{2}+a)& =(\color{red}{p}+\color{orange}{\frac{17}{14}}).(\color{green}{a}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{2}p+\frac{17}{14}a+\frac{17}{14}.\frac{13}{2}& \text{Uitwerken } \\ & =ap+\frac{13}{2}p+\frac{17}{14}a+\frac{221}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{4}{12})(\frac{-19}{16}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{16}p-\frac{1}{3}p-\frac{1}{3}.\frac{19}{16}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{16})+(\frac{-1}{3}))p-\frac{19}{48} & \text{Neem samen} \\ &=-p^2-\frac{73}{48}p-\frac{19}{48} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{1}{14}+b)(\frac{-17}{5}-x)& =(\color{red}{b}+\color{orange}{\frac{1}{14}}).(\color{green}{-x}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{1}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{17}{5}b-\frac{1}{14}x-\frac{1}{14}.\frac{17}{5}& \text{Uitwerken } \\ & =-bx-\frac{17}{5}b-\frac{1}{14}x-\frac{17}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{17}{7}+b)(\frac{-4}{6}+q)& =(\color{red}{b}+\color{orange}{\frac{17}{7}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{3}b+\frac{17}{7}q-\frac{17}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =bq-\frac{2}{3}b+\frac{17}{7}q-\frac{34}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-4}{8}+a)(a+\frac{17}{15})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{17}{15}a-\frac{1}{2}a-\frac{1}{2}.\frac{17}{15}& \text{Uitwerken } \\ & =a^2+(\frac{17}{15}+(\frac{-1}{2}))a-(\frac{-17}{30}) & \text{Neem samen} \\ &=a^2+\frac{19}{30}a-(\frac{-17}{30}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p+\frac{-8}{2})(\frac{-8}{6}-a)& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{-a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-4)} . \color{green}{(-a)} + \color{orange}{(-4)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{4}{3}p+4a+4.\frac{4}{3}& \text{Uitwerken } \\ & =-ap-\frac{4}{3}p+4a+\frac{16}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{7}{5}+b)(p+\frac{-13}{15})& =(\color{red}{b}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{15}b+\frac{7}{5}p-\frac{7}{5}.\frac{13}{15}& \text{Uitwerken } \\ & =bp-\frac{13}{15}b+\frac{7}{5}p-\frac{91}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{7}{19})(\frac{-3}{4}-q)& =(\color{red}{x}+\color{orange}{\frac{-7}{19}}).(\color{green}{-q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{4}x+\frac{7}{19}q+\frac{7}{19}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx-\frac{3}{4}x+\frac{7}{19}q+\frac{21}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)