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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-11}{5})(b-\frac{-16}{20})& =(\color{red}{b}+\color{orange}{\frac{-11}{5}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{5}b-\frac{11}{5}b-\frac{11}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =b^2+(\frac{4}{5}+(\frac{-11}{5}))b-(\frac{-44}{25}) & \text{Neem samen} \\ &=b^2-\frac{7}{5}b-(\frac{-44}{25}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{6}{10}-x)(\frac{17}{7}+q)& =(\color{red}{-x}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{7}x+\frac{3}{5}q+\frac{3}{5}.\frac{17}{7}& \text{Uitwerken } \\ & =-qx-\frac{17}{7}x+\frac{3}{5}q+\frac{51}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{20}{3}+a)(\frac{13}{19}+p)& =(\color{red}{a}+\color{orange}{\frac{20}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{20}{3})} . \color{green}{(p)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{19}a+\frac{20}{3}p+\frac{20}{3}.\frac{13}{19}& \text{Uitwerken } \\ & =ap+\frac{13}{19}a+\frac{20}{3}p+\frac{260}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{6}{17}-a)(b+\frac{-19}{17})& =(\color{red}{-a}+\color{orange}{\frac{6}{17}}).(\color{green}{b}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{17}a+\frac{6}{17}b-\frac{6}{17}.\frac{19}{17}& \text{Uitwerken } \\ & =-ab+\frac{19}{17}a+\frac{6}{17}b-\frac{114}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a+\frac{11}{20})(b+\frac{-3}{14})& =(\color{red}{a}+\color{orange}{\frac{11}{20}}).(\color{green}{b}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{11}{20})} . \color{green}{(b)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{14}a+\frac{11}{20}b-\frac{11}{20}.\frac{3}{14}& \text{Uitwerken } \\ & =ab-\frac{3}{14}a+\frac{11}{20}b-\frac{33}{280} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{8}{9})(\frac{-16}{3}+x)& =(\color{red}{q}+\color{orange}{\frac{8}{9}}).(\color{green}{x}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{3}q+\frac{8}{9}x-\frac{8}{9}.\frac{16}{3}& \text{Uitwerken } \\ & =qx-\frac{16}{3}q+\frac{8}{9}x-\frac{128}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{-16}{9})(a+\frac{8}{3})& =(\color{red}{q}+\color{orange}{\frac{-16}{9}}).(\color{green}{a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{3}q-\frac{16}{9}a-\frac{16}{9}.\frac{8}{3}& \text{Uitwerken } \\ & =aq+\frac{8}{3}q-\frac{16}{9}a-\frac{128}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{11}{15})(x+\frac{9}{12})& =(\color{red}{q}+\color{orange}{\frac{11}{15}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{11}{15})} . \color{green}{(x)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{4}q+\frac{11}{15}x+\frac{11}{15}.\frac{3}{4}& \text{Uitwerken } \\ & =qx+\frac{3}{4}q+\frac{11}{15}x+\frac{33}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{4}q+\frac{11}{15}x+\frac{11}{20} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}((-2)+q)((-18)+p)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{(-18)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-18)} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = pq-18q-2p+2.18& \text{Uitwerken } \\ & =pq-18q-2p+36 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{11}{8}+x)(b-\frac{-9}{18})& =(\color{red}{x}+\color{orange}{\frac{11}{8}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x+\frac{11}{8}b+\frac{11}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x+\frac{11}{8}b+\frac{11}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-18}{9}-q)(q+\frac{1}{9})& =(\color{red}{-q}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{9}q-2q-2.\frac{1}{9}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{9})+(-2))q-\frac{2}{9} & \text{Neem samen} \\ &=-q^2-\frac{19}{9}q-\frac{2}{9} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(a+\frac{10}{19})(\frac{-11}{17}+p)& =(\color{red}{a}+\color{orange}{\frac{10}{19}}).(\color{green}{p}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{17}a+\frac{10}{19}p-\frac{10}{19}.\frac{11}{17}& \text{Uitwerken } \\ & =ap-\frac{11}{17}a+\frac{10}{19}p-\frac{110}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)