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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{4}{20})(\frac{-15}{2}-p)& =(\color{red}{q}+\color{orange}{\frac{-1}{5}}).(\color{green}{-p}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{15}{2}q+\frac{1}{5}p+\frac{1}{5}.\frac{15}{2}& \text{Uitwerken } \\ & =-pq-\frac{15}{2}q+\frac{1}{5}p+\frac{15}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{15}{2}q+\frac{1}{5}p+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{1}{11}+x)(\frac{7}{5}-a)& =(\color{red}{x}+\color{orange}{\frac{1}{11}}).(\color{green}{-a}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{1}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{5}x-\frac{1}{11}a+\frac{1}{11}.\frac{7}{5}& \text{Uitwerken } \\ & =-ax+\frac{7}{5}x-\frac{1}{11}a+\frac{7}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{4}{19}+p)(\frac{-7}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{4}{19}}).(\color{green}{b}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{4}{19})} . \color{green}{(b)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{4}p+\frac{4}{19}b-\frac{4}{19}.\frac{7}{4}& \text{Uitwerken } \\ & =bp-\frac{7}{4}p+\frac{4}{19}b-\frac{28}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{4}p+\frac{4}{19}b-\frac{7}{19} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{6}{2}-b)(\frac{2}{20}+q)& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{10}b+3q+3.\frac{1}{10}& \text{Uitwerken } \\ & =-bq-\frac{1}{10}b+3q+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p-\frac{-18}{10})(\frac{-3}{3}-p)& =(\color{red}{p}+\color{orange}{\frac{9}{5}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{9}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pp-1p-\frac{9}{5}p-\frac{9}{5}.1& \text{Uitwerken } \\ & =-p^2+((-1)+(\frac{-9}{5}))p-\frac{9}{5} & \text{Neem samen} \\ &=-p^2-\frac{14}{5}p-\frac{9}{5} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{14}{14}-p)(\frac{-5}{7}+b)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{7}p+1b-1.\frac{5}{7}& \text{Uitwerken } \\ & =-bp+\frac{5}{7}p+1b-\frac{5}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{-13}{13})(x-\frac{13}{6})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{6}q-1x+1.\frac{13}{6}& \text{Uitwerken } \\ & =qx-\frac{13}{6}q-1x+\frac{13}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{-11}{17})(\frac{-2}{2}+p)& =(\color{red}{q}+\color{orange}{\frac{-11}{17}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q-\frac{11}{17}p+\frac{11}{17}.1& \text{Uitwerken } \\ & =pq-1q-\frac{11}{17}p+\frac{11}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{-10}{11})(x+\frac{13}{16})& =(\color{red}{q}+\color{orange}{\frac{-10}{11}}).(\color{green}{x}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{16}q-\frac{10}{11}x-\frac{10}{11}.\frac{13}{16}& \text{Uitwerken } \\ & =qx+\frac{13}{16}q-\frac{10}{11}x-\frac{130}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{16}q-\frac{10}{11}x-\frac{65}{88} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x-18)(q+\frac{-8}{2})& =(\color{red}{x}+\color{orange}{(-18)}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(-18)} . \color{green}{(q)} + \color{orange}{(-18)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4x-18q+18.4& \text{Uitwerken } \\ & =qx-4x-18q+72 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-20}{9})(\frac{15}{20}+b)& =(\color{red}{a}+\color{orange}{\frac{20}{9}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{20}{9})} . \color{green}{(b)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{4}a+\frac{20}{9}b+\frac{20}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =ab+\frac{3}{4}a+\frac{20}{9}b+\frac{60}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{4}a+\frac{20}{9}b+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-1}{19}-a)(\frac{-4}{8}-b)& =(\color{red}{-a}+\color{orange}{\frac{-1}{19}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a+\frac{1}{19}b+\frac{1}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a+\frac{1}{19}b+\frac{1}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)