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

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

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Verbetersleutel

1. \(\begin{align}(b-\frac{-2}{3})(5+q)& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bq+5b+\frac{2}{3}q+\frac{2}{3}.5& \text{Uitwerken } \\ & =bq+5b+\frac{2}{3}q+\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{19}-x)(\frac{20}{14}-a)& =(\color{red}{-x}+\color{orange}{\frac{-9}{19}}).(\color{green}{-a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{7}x+\frac{9}{19}a-\frac{9}{19}.\frac{10}{7}& \text{Uitwerken } \\ & =ax-\frac{10}{7}x+\frac{9}{19}a-\frac{90}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{4}{12})(x+\frac{19}{4})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{4}q+\frac{1}{3}x+\frac{1}{3}.\frac{19}{4}& \text{Uitwerken } \\ & =qx+\frac{19}{4}q+\frac{1}{3}x+\frac{19}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{7}{5})(b+\frac{9}{2})& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{7}{5})} . \color{green}{(b)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{2}a+\frac{7}{5}b+\frac{7}{5}.\frac{9}{2}& \text{Uitwerken } \\ & =ab+\frac{9}{2}a+\frac{7}{5}b+\frac{63}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{1}{18}+p)(a+\frac{6}{11})& =(\color{red}{p}+\color{orange}{\frac{1}{18}}).(\color{green}{a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{1}{18})} . \color{green}{(a)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{11}p+\frac{1}{18}a+\frac{1}{18}.\frac{6}{11}& \text{Uitwerken } \\ & =ap+\frac{6}{11}p+\frac{1}{18}a+\frac{6}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{6}{11}p+\frac{1}{18}a+\frac{1}{33} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{18}{6}+q)(a-\frac{-16}{9})& =(\color{red}{q}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{9}q+3a+3.\frac{16}{9}& \text{Uitwerken } \\ & =aq+\frac{16}{9}q+3a+\frac{48}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{16}{9}q+3a+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x+\frac{13}{8})(\frac{7}{3}+x)& =(\color{red}{x}+\color{orange}{\frac{13}{8}}).(\color{green}{x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{13}{8})} . \color{green}{(x)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{3}x+\frac{13}{8}x+\frac{13}{8}.\frac{7}{3}& \text{Uitwerken } \\ & =x^2+(\frac{7}{3}+\frac{13}{8})x+\frac{91}{24} & \text{Neem samen} \\ &=x^2+\frac{95}{24}x+\frac{91}{24} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(q+\frac{-10}{5})(q-\frac{8}{6})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{3}q-2q+2.\frac{4}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{3})+(-2))q+\frac{8}{3} & \text{Neem samen} \\ &=q^2-\frac{10}{3}q+\frac{8}{3} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{16}{16}-q)(\frac{-17}{8}+p)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{8}q+1p-1.\frac{17}{8}& \text{Uitwerken } \\ & =-pq+\frac{17}{8}q+1p-\frac{17}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{9}{13}-a)(\frac{20}{14}-a)& =(\color{red}{-a}+\color{orange}{\frac{9}{13}}).(\color{green}{-a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{9}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{10}{7}a-\frac{9}{13}a+\frac{9}{13}.\frac{10}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-10}{7})+(\frac{-9}{13}))a+\frac{90}{91} & \text{Neem samen} \\ &=a^2-\frac{193}{91}a+\frac{90}{91} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(q-18)(p+11)& =(\color{red}{q}+\color{orange}{(-18)}).(\color{green}{p}+\color{blue}{11})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(11)} + \color{orange}{(-18)} . \color{green}{(p)} + \color{orange}{(-18)} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = pq+11q-18p-18.11& \text{Uitwerken } \\ & =pq+11q-18p-198 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{15}{12}+b)(x+\frac{19}{20})& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{20}b+\frac{5}{4}x+\frac{5}{4}.\frac{19}{20}& \text{Uitwerken } \\ & =bx+\frac{19}{20}b+\frac{5}{4}x+\frac{95}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{19}{20}b+\frac{5}{4}x+\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)