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

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

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Verbetersleutel

1. \(\begin{align}(q+\frac{16}{13})(\frac{18}{6}-x)& =(\color{red}{q}+\color{orange}{\frac{16}{13}}).(\color{green}{-x}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{16}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -qx+3q-\frac{16}{13}x+\frac{16}{13}.3& \text{Uitwerken } \\ & =-qx+3q-\frac{16}{13}x+\frac{48}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{-7}{9})((-20)+a)& =(\color{red}{b}+\color{orange}{\frac{-7}{9}}).(\color{green}{a}+\color{blue}{(-20)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-20)} + \color{orange}{(\frac{-7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = ab-20b-\frac{7}{9}a+\frac{7}{9}.20& \text{Uitwerken } \\ & =ab-20b-\frac{7}{9}a+\frac{140}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{16}{12})(\frac{-16}{13}+p)& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{13}x-\frac{4}{3}p+\frac{4}{3}.\frac{16}{13}& \text{Uitwerken } \\ & =px-\frac{16}{13}x-\frac{4}{3}p+\frac{64}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{20}{13}-q)(\frac{-4}{19}-a)& =(\color{red}{-q}+\color{orange}{\frac{20}{13}}).(\color{green}{-a}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{20}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{19}q-\frac{20}{13}a-\frac{20}{13}.\frac{4}{19}& \text{Uitwerken } \\ & =aq+\frac{4}{19}q-\frac{20}{13}a-\frac{80}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{8}{19})(\frac{-15}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{-8}{19}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-8}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aa-3a+\frac{8}{19}a+\frac{8}{19}.3& \text{Uitwerken } \\ & =-a^2+((-3)+\frac{8}{19})a+(\frac{-24}{19}) & \text{Neem samen} \\ &=-a^2-\frac{49}{19}a+(\frac{-24}{19}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{15}{7}-q)(b+\frac{-14}{16})& =(\color{red}{-q}+\color{orange}{\frac{15}{7}}).(\color{green}{b}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{15}{7})} . \color{green}{(b)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{8}q+\frac{15}{7}b-\frac{15}{7}.\frac{7}{8}& \text{Uitwerken } \\ & =-bq+\frac{7}{8}q+\frac{15}{7}b-\frac{105}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{7}{8}q+\frac{15}{7}b-\frac{15}{8} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{7}{3}+x)(q+\frac{-5}{14})& =(\color{red}{x}+\color{orange}{\frac{7}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{14}x+\frac{7}{3}q-\frac{7}{3}.\frac{5}{14}& \text{Uitwerken } \\ & =qx-\frac{5}{14}x+\frac{7}{3}q-\frac{35}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{14}x+\frac{7}{3}q-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{18}{6}+b)(\frac{16}{9}-p)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{-p}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(3)} . \color{green}{(-p)} + \color{orange}{(3)} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{16}{9}b-3p+3.\frac{16}{9}& \text{Uitwerken } \\ & =-bp+\frac{16}{9}b-3p+\frac{48}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{16}{9}b-3p+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-\frac{-16}{3})(\frac{-9}{4}-p)& =(\color{red}{x}+\color{orange}{\frac{16}{3}}).(\color{green}{-p}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{16}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{4}x-\frac{16}{3}p-\frac{16}{3}.\frac{9}{4}& \text{Uitwerken } \\ & =-px-\frac{9}{4}x-\frac{16}{3}p-\frac{144}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{9}{4}x-\frac{16}{3}p-12 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(b-\frac{-4}{13})(p+\frac{16}{17})& =(\color{red}{b}+\color{orange}{\frac{4}{13}}).(\color{green}{p}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{17}b+\frac{4}{13}p+\frac{4}{13}.\frac{16}{17}& \text{Uitwerken } \\ & =bp+\frac{16}{17}b+\frac{4}{13}p+\frac{64}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(19+b)(a+\frac{-8}{4})& =(\color{red}{b}+\color{orange}{19}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(19)} . \color{green}{(a)} + \color{orange}{(19)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b+19a-19.2& \text{Uitwerken } \\ & =ab-2b+19a-38 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{17}{12}+a)(x-\frac{6}{15})& =(\color{red}{a}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{5}a+\frac{17}{12}x-\frac{17}{12}.\frac{2}{5}& \text{Uitwerken } \\ & =ax-\frac{2}{5}a+\frac{17}{12}x-\frac{34}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{2}{5}a+\frac{17}{12}x-\frac{17}{30} & \text{Vereenvoudig} \\\end{align}\)