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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{5}{4})(\frac{13}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pq+1q-\frac{5}{4}p+\frac{5}{4}.1& \text{Uitwerken } \\ & =-pq+1q-\frac{5}{4}p+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-12}{4}+q)(\frac{-2}{20}+p)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{10}q-3p+3.\frac{1}{10}& \text{Uitwerken } \\ & =pq-\frac{1}{10}q-3p+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{16}{3})(a-\frac{-1}{8})& =(\color{red}{x}+\color{orange}{\frac{16}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{16}{3})} . \color{green}{(a)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{8}x+\frac{16}{3}a+\frac{16}{3}.\frac{1}{8}& \text{Uitwerken } \\ & =ax+\frac{1}{8}x+\frac{16}{3}a+\frac{16}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{8}x+\frac{16}{3}a+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{16}{11}+q)(\frac{-18}{18}-a)& =(\color{red}{q}+\color{orange}{\frac{16}{11}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{16}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1q-\frac{16}{11}a-\frac{16}{11}.1& \text{Uitwerken } \\ & =-aq-1q-\frac{16}{11}a-\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{3}-a)(q-\frac{-6}{18})& =(\color{red}{-a}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{3}a+6q+6.\frac{1}{3}& \text{Uitwerken } \\ & =-aq-\frac{1}{3}a+6q+\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{3}a+6q+2 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-4}{6}+a)(q+\frac{18}{9})& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a-\frac{2}{3}q-\frac{2}{3}.2& \text{Uitwerken } \\ & =aq+2a-\frac{2}{3}q-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{7}{18})(\frac{-19}{8}-b)& =(\color{red}{b}+\color{orange}{\frac{7}{18}}).(\color{green}{-b}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{7}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{8}b-\frac{7}{18}b-\frac{7}{18}.\frac{19}{8}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{8})+(\frac{-7}{18}))b-\frac{133}{144} & \text{Neem samen} \\ &=-b^2-\frac{199}{72}b-\frac{133}{144} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(b-\frac{12}{11})(\frac{17}{17}+a)& =(\color{red}{b}+\color{orange}{\frac{-12}{11}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b-\frac{12}{11}a-\frac{12}{11}.1& \text{Uitwerken } \\ & =ab+1b-\frac{12}{11}a-\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{14}{6}-x)(\frac{15}{20}-q)& =(\color{red}{-x}+\color{orange}{\frac{7}{3}}).(\color{green}{-q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{4}x-\frac{7}{3}q+\frac{7}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =qx-\frac{3}{4}x-\frac{7}{3}q+\frac{21}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{4}x-\frac{7}{3}q+\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-16}{7}+x)(\frac{12}{2}-b)& =(\color{red}{x}+\color{orange}{\frac{-16}{7}}).(\color{green}{-b}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(\frac{-16}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -bx+6x+\frac{16}{7}b-\frac{16}{7}.6& \text{Uitwerken } \\ & =-bx+6x+\frac{16}{7}b-\frac{96}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-8}{4}-a)(\frac{8}{10}+b)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{5}a-2b-2.\frac{4}{5}& \text{Uitwerken } \\ & =-ab-\frac{4}{5}a-2b-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{-15}{13})(b+\frac{4}{16})& =(\color{red}{b}+\color{orange}{\frac{-15}{13}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{4}b-\frac{15}{13}b-\frac{15}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =b^2+(\frac{1}{4}+(\frac{-15}{13}))b-(\frac{-15}{52}) & \text{Neem samen} \\ &=b^2-\frac{47}{52}b-(\frac{-15}{52}) & \text{Maak de som} \\\end{align}\)