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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{5}{15})(\frac{7}{20}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{7}{20}p-\frac{1}{3}p+\frac{1}{3}.\frac{7}{20}& \text{Uitwerken } \\ & =-p^2+(\frac{7}{20}+(\frac{-1}{3}))p+(\frac{-7}{60}) & \text{Neem samen} \\ &=-p^2+\frac{1}{60}p+(\frac{-7}{60}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(p+\frac{8}{4})(\frac{19}{12}-q)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{19}{12}p-2q+2.\frac{19}{12}& \text{Uitwerken } \\ & =-pq+\frac{19}{12}p-2q+\frac{38}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{19}{12}p-2q+\frac{19}{6} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-18}{10}+x)(\frac{-5}{9}-b)& =(\color{red}{x}+\color{orange}{\frac{-9}{5}}).(\color{green}{-b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{9}x+\frac{9}{5}b+\frac{9}{5}.\frac{5}{9}& \text{Uitwerken } \\ & =-bx-\frac{5}{9}x+\frac{9}{5}b+\frac{45}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{9}x+\frac{9}{5}b+1 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{-2}{5})(a-\frac{-5}{5})& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p-\frac{2}{5}a-\frac{2}{5}.1& \text{Uitwerken } \\ & =ap+1p-\frac{2}{5}a-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{1}{17})(b+\frac{-15}{6})& =(\color{red}{a}+\color{orange}{\frac{-1}{17}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{2}a-\frac{1}{17}b+\frac{1}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =ab-\frac{5}{2}a-\frac{1}{17}b+\frac{5}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-6}{6}-x)(\frac{9}{5}-p)& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{5}x+1p-1.\frac{9}{5}& \text{Uitwerken } \\ & =px-\frac{9}{5}x+1p-\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{-1}{5})(\frac{-8}{3}+q)& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{8}{3}q+\frac{1}{5}q-\frac{1}{5}.\frac{8}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-8}{3})+\frac{1}{5})q-(\frac{-8}{15}) & \text{Neem samen} \\ &=q^2-\frac{37}{15}q-(\frac{-8}{15}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(x+\frac{3}{20})(a-\frac{9}{20})& =(\color{red}{x}+\color{orange}{\frac{3}{20}}).(\color{green}{a}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{3}{20})} . \color{green}{(a)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{20}x+\frac{3}{20}a-\frac{3}{20}.\frac{9}{20}& \text{Uitwerken } \\ & =ax-\frac{9}{20}x+\frac{3}{20}a-\frac{27}{400} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-14}{14}+a)(a-\frac{-5}{4})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{4}a-1a-1.\frac{5}{4}& \text{Uitwerken } \\ & =a^2+(\frac{5}{4}+(-1))a-(\frac{-5}{4}) & \text{Neem samen} \\ &=a^2+\frac{1}{4}a-(\frac{-5}{4}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a+\frac{16}{6})(\frac{-10}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{3}a+\frac{8}{3}p-\frac{8}{3}.\frac{5}{3}& \text{Uitwerken } \\ & =ap-\frac{5}{3}a+\frac{8}{3}p-\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{-14}{6})(b+(-14))& =(\color{red}{a}+\color{orange}{\frac{-7}{3}}).(\color{green}{b}+\color{blue}{(-14)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-14)} + \color{orange}{(\frac{-7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = ab-14a-\frac{7}{3}b+\frac{7}{3}.14& \text{Uitwerken } \\ & =ab-14a-\frac{7}{3}b+\frac{98}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-9}{9})(a+\frac{-1}{2})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{2}q+1a-1.\frac{1}{2}& \text{Uitwerken } \\ & =aq-\frac{1}{2}q+1a-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)