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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-3}{12}+p)(q-\frac{-10}{18})& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{9}p-\frac{1}{4}q-\frac{1}{4}.\frac{5}{9}& \text{Uitwerken } \\ & =pq+\frac{5}{9}p-\frac{1}{4}q-\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{20}{6}-x)(p-\frac{-18}{18})& =(\color{red}{-x}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px-1x+\frac{10}{3}p+\frac{10}{3}.1& \text{Uitwerken } \\ & =-px-1x+\frac{10}{3}p+\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-(-12))(\frac{3}{9}+a)& =(\color{red}{b}+\color{orange}{12}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(12)} . \color{green}{(a)} + \color{orange}{(12)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}b+12a+12.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}b+12a+\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{3}b+12a+4 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{5}{4}-q)(b+\frac{-6}{19})& =(\color{red}{-q}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{6}{19}q+\frac{5}{4}b-\frac{5}{4}.\frac{6}{19}& \text{Uitwerken } \\ & =-bq+\frac{6}{19}q+\frac{5}{4}b-\frac{30}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{6}{19}q+\frac{5}{4}b-\frac{15}{38} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b-\frac{8}{15})(p-\frac{-16}{5})& =(\color{red}{b}+\color{orange}{\frac{-8}{15}}).(\color{green}{p}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{5}b-\frac{8}{15}p-\frac{8}{15}.\frac{16}{5}& \text{Uitwerken } \\ & =bp+\frac{16}{5}b-\frac{8}{15}p-\frac{128}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+6)(\frac{16}{20}-q)& =(\color{red}{q}+\color{orange}{6}).(\color{green}{-q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(6)} . \color{green}{(-q)} + \color{orange}{(6)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{4}{5}q-6q+6.\frac{4}{5}& \text{Uitwerken } \\ & =-q^2+(\frac{4}{5}+(-6))q+(\frac{-24}{5}) & \text{Neem samen} \\ &=-q^2-\frac{26}{5}q+(\frac{-24}{5}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-15}{17}-q)(b+(-18))& =(\color{red}{-q}+\color{orange}{\frac{-15}{17}}).(\color{green}{b}+\color{blue}{(-18)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-18)} + \color{orange}{(\frac{-15}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -bq+18q-\frac{15}{17}b+\frac{15}{17}.18& \text{Uitwerken } \\ & =-bq+18q-\frac{15}{17}b+\frac{270}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{-12}{10})(\frac{-20}{10}-b)& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{-b}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bp-2p-\frac{6}{5}b-\frac{6}{5}.2& \text{Uitwerken } \\ & =-bp-2p-\frac{6}{5}b-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+(-4))(p-\frac{14}{12})& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{6}q-4p+4.\frac{7}{6}& \text{Uitwerken } \\ & =pq-\frac{7}{6}q-4p+\frac{28}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{6}q-4p+\frac{14}{3} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{6}{13})(q+\frac{18}{8})& =(\color{red}{p}+\color{orange}{\frac{6}{13}}).(\color{green}{q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{4}p+\frac{6}{13}q+\frac{6}{13}.\frac{9}{4}& \text{Uitwerken } \\ & =pq+\frac{9}{4}p+\frac{6}{13}q+\frac{54}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{9}{4}p+\frac{6}{13}q+\frac{27}{26} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{19}-b)(\frac{17}{17}-b)& =(\color{red}{-b}+\color{orange}{\frac{-7}{19}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{-7}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bb-1b+\frac{7}{19}b-\frac{7}{19}.1& \text{Uitwerken } \\ & =b^2+((-1)+\frac{7}{19})b-(\frac{-7}{19}) & \text{Neem samen} \\ &=b^2-\frac{12}{19}b-(\frac{-7}{19}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{13}-p)(\frac{-9}{2}-b)& =(\color{red}{-p}+\color{orange}{\frac{-5}{13}}).(\color{green}{-b}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{2}p+\frac{5}{13}b+\frac{5}{13}.\frac{9}{2}& \text{Uitwerken } \\ & =bp+\frac{9}{2}p+\frac{5}{13}b+\frac{45}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)