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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-16}{2})(\frac{4}{20}-a)& =(\color{red}{p}+\color{orange}{(-8)}).(\color{green}{-a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(-8)} . \color{green}{(-a)} + \color{orange}{(-8)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{5}p+8a-8.\frac{1}{5}& \text{Uitwerken } \\ & =-ap+\frac{1}{5}p+8a-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{19}{13})(\frac{-3}{18}-q)& =(\color{red}{q}+\color{orange}{\frac{19}{13}}).(\color{green}{-q}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{19}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{6}q-\frac{19}{13}q-\frac{19}{13}.\frac{1}{6}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{6})+(\frac{-19}{13}))q-\frac{19}{78} & \text{Neem samen} \\ &=-q^2-\frac{127}{78}q-\frac{19}{78} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(q-\frac{10}{2})(\frac{-17}{15}-p)& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{-p}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(-5)} . \color{green}{(-p)} + \color{orange}{(-5)} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{17}{15}q+5p+5.\frac{17}{15}& \text{Uitwerken } \\ & =-pq-\frac{17}{15}q+5p+\frac{85}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{17}{15}q+5p+\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-18}{8}+q)(a-\frac{-12}{18})& =(\color{red}{q}+\color{orange}{\frac{-9}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{3}q-\frac{9}{4}a-\frac{9}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =aq+\frac{2}{3}q-\frac{9}{4}a-\frac{18}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{2}{3}q-\frac{9}{4}a-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{6}{18}-p)(\frac{-16}{12}+q)& =(\color{red}{-p}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{4}{3}p+\frac{1}{3}q-\frac{1}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =-pq+\frac{4}{3}p+\frac{1}{3}q-\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{1}{13})(\frac{-1}{11}-b)& =(\color{red}{a}+\color{orange}{\frac{-1}{13}}).(\color{green}{-b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{11}a+\frac{1}{13}b+\frac{1}{13}.\frac{1}{11}& \text{Uitwerken } \\ & =-ab-\frac{1}{11}a+\frac{1}{13}b+\frac{1}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{18}-p)(x+\frac{-10}{9})& =(\color{red}{-p}+\color{orange}{\frac{-13}{18}}).(\color{green}{x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{9}p-\frac{13}{18}x+\frac{13}{18}.\frac{10}{9}& \text{Uitwerken } \\ & =-px+\frac{10}{9}p-\frac{13}{18}x+\frac{130}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{10}{9}p-\frac{13}{18}x+\frac{65}{81} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-19}{8}+b)(\frac{19}{4}+b)& =(\color{red}{b}+\color{orange}{\frac{-19}{8}}).(\color{green}{b}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{19}{4}b-\frac{19}{8}b-\frac{19}{8}.\frac{19}{4}& \text{Uitwerken } \\ & =b^2+(\frac{19}{4}+(\frac{-19}{8}))b-(\frac{-361}{32}) & \text{Neem samen} \\ &=b^2+\frac{19}{8}b-(\frac{-361}{32}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(p+\frac{-4}{10})((-15)+b)& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{(-15)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-15)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = bp-15p-\frac{2}{5}b+\frac{2}{5}.15& \text{Uitwerken } \\ & =bp-15p-\frac{2}{5}b+\frac{30}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-15p-\frac{2}{5}b+6 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{17}{18})(b+\frac{12}{11})& =(\color{red}{p}+\color{orange}{\frac{-17}{18}}).(\color{green}{b}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{11}p-\frac{17}{18}b-\frac{17}{18}.\frac{12}{11}& \text{Uitwerken } \\ & =bp+\frac{12}{11}p-\frac{17}{18}b-\frac{204}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{12}{11}p-\frac{17}{18}b-\frac{34}{33} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a+\frac{2}{2})(b+\frac{-19}{20})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{20}a+1b-1.\frac{19}{20}& \text{Uitwerken } \\ & =ab-\frac{19}{20}a+1b-\frac{19}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}((-10)-b)(\frac{-9}{3}-a)& =(\color{red}{-b}+\color{orange}{(-10)}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(-3)} + \color{orange}{(-10)} . \color{green}{(-a)} + \color{orange}{(-10)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ab+3b+10a+10.3& \text{Uitwerken } \\ & =ab+3b+10a+30 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)