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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{11}{11}-x)(\frac{9}{19}+p)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{19}x+1p+1.\frac{9}{19}& \text{Uitwerken } \\ & =-px-\frac{9}{19}x+1p+\frac{9}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{-7}{14})(p-\frac{-18}{8})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{4}a-\frac{1}{2}p-\frac{1}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =ap+\frac{9}{4}a-\frac{1}{2}p-\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{9}-p)(b+14)& =(\color{red}{-p}+\color{orange}{\frac{-1}{9}}).(\color{green}{b}+\color{blue}{14})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(14)} + \color{orange}{(\frac{-1}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = -bp-14p-\frac{1}{9}b-\frac{1}{9}.14& \text{Uitwerken } \\ & =-bp-14p-\frac{1}{9}b-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-6}{7}+q)(\frac{-9}{20}-p)& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{-p}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{20}q+\frac{6}{7}p+\frac{6}{7}.\frac{9}{20}& \text{Uitwerken } \\ & =-pq-\frac{9}{20}q+\frac{6}{7}p+\frac{54}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{9}{20}q+\frac{6}{7}p+\frac{27}{70} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{8}{20}-b)(\frac{-9}{4}+a)& =(\color{red}{-b}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{9}{4}b+\frac{2}{5}a-\frac{2}{5}.\frac{9}{4}& \text{Uitwerken } \\ & =-ab+\frac{9}{4}b+\frac{2}{5}a-\frac{18}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{9}{4}b+\frac{2}{5}a-\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{11}{9}-x)(q+\frac{-1}{19})& =(\color{red}{-x}+\color{orange}{\frac{11}{9}}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{11}{9})} . \color{green}{(q)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{19}x+\frac{11}{9}q-\frac{11}{9}.\frac{1}{19}& \text{Uitwerken } \\ & =-qx+\frac{1}{19}x+\frac{11}{9}q-\frac{11}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-8}{10}-p)(a-\frac{-13}{9})& =(\color{red}{-p}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{9}p-\frac{4}{5}a-\frac{4}{5}.\frac{13}{9}& \text{Uitwerken } \\ & =-ap-\frac{13}{9}p-\frac{4}{5}a-\frac{52}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+(-14))(b-\frac{2}{3})& =(\color{red}{a}+\color{orange}{(-14)}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-14)} . \color{green}{(b)} + \color{orange}{(-14)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{3}a-14b+14.\frac{2}{3}& \text{Uitwerken } \\ & =ab-\frac{2}{3}a-14b+\frac{28}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-8}{20}-q)(q+\frac{-16}{18})& =(\color{red}{-q}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{8}{9}q-\frac{2}{5}q+\frac{2}{5}.\frac{8}{9}& \text{Uitwerken } \\ & =-q^2+(\frac{8}{9}+(\frac{-2}{5}))q+(\frac{-16}{45}) & \text{Neem samen} \\ &=-q^2+\frac{22}{45}q+(\frac{-16}{45}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-16}{4}+p)(b-20)& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{(-20)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-20)} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = bp-20p-4b+4.20& \text{Uitwerken } \\ & =bp-20p-4b+80 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{14}{20})(\frac{-13}{19}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{10}}).(\color{green}{-b}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{13}{19}b+\frac{7}{10}b+\frac{7}{10}.\frac{13}{19}& \text{Uitwerken } \\ & =-b^2+((\frac{-13}{19})+\frac{7}{10})b+(\frac{-91}{190}) & \text{Neem samen} \\ &=-b^2+\frac{3}{190}b+(\frac{-91}{190}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-6}{16}-x)(\frac{4}{10}-q)& =(\color{red}{-x}+\color{orange}{\frac{-3}{8}}).(\color{green}{-q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{5}x+\frac{3}{8}q-\frac{3}{8}.\frac{2}{5}& \text{Uitwerken } \\ & =qx-\frac{2}{5}x+\frac{3}{8}q-\frac{6}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{2}{5}x+\frac{3}{8}q-\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)