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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{18}{3}-b)(p+\frac{-19}{20})& =(\color{red}{-b}+\color{orange}{6}).(\color{green}{p}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{20}b+6p-6.\frac{19}{20}& \text{Uitwerken } \\ & =-bp+\frac{19}{20}b+6p-\frac{114}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{19}{20}b+6p-\frac{57}{10} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b-\frac{-1}{8})(\frac{-19}{3}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{8}}).(\color{green}{x}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(x)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{3}b+\frac{1}{8}x-\frac{1}{8}.\frac{19}{3}& \text{Uitwerken } \\ & =bx-\frac{19}{3}b+\frac{1}{8}x-\frac{19}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{19}{11})(q-\frac{-16}{20})& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{5}b-\frac{19}{11}q-\frac{19}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =bq+\frac{4}{5}b-\frac{19}{11}q-\frac{76}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-7}{2})(\frac{8}{11}+b)& =(\color{red}{q}+\color{orange}{\frac{7}{2}}).(\color{green}{b}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{11}q+\frac{7}{2}b+\frac{7}{2}.\frac{8}{11}& \text{Uitwerken } \\ & =bq+\frac{8}{11}q+\frac{7}{2}b+\frac{56}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{8}{11}q+\frac{7}{2}b+\frac{28}{11} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b-\frac{-12}{9})(b+\frac{-1}{5})& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{5}b+\frac{4}{3}b-\frac{4}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{5})+\frac{4}{3})b-(\frac{-4}{15}) & \text{Neem samen} \\ &=b^2+\frac{17}{15}b-(\frac{-4}{15}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{10}-a)(\frac{-9}{15}+b)& =(\color{red}{-a}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{5}a-\frac{7}{10}b+\frac{7}{10}.\frac{3}{5}& \text{Uitwerken } \\ & =-ab+\frac{3}{5}a-\frac{7}{10}b+\frac{21}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-7}{16}+b)(\frac{-13}{5}-q)& =(\color{red}{b}+\color{orange}{\frac{-7}{16}}).(\color{green}{-q}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{5}b+\frac{7}{16}q+\frac{7}{16}.\frac{13}{5}& \text{Uitwerken } \\ & =-bq-\frac{13}{5}b+\frac{7}{16}q+\frac{91}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{-2}{5})((-6)-x)& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{-x}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-6)} + \color{orange}{(\frac{2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -qx-6q-\frac{2}{5}x-\frac{2}{5}.6& \text{Uitwerken } \\ & =-qx-6q-\frac{2}{5}x-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-2}{2}-a)(\frac{-7}{4}-b)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{4}a+1b+1.\frac{7}{4}& \text{Uitwerken } \\ & =ab+\frac{7}{4}a+1b+\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{-7}{14})(\frac{-20}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{3}b+\frac{1}{2}q-\frac{1}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =bq-\frac{5}{3}b+\frac{1}{2}q-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{-8}{2})(a+\frac{-20}{4})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ab-5b+4a-4.5& \text{Uitwerken } \\ & =ab-5b+4a-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-16}{2}+a)(a+\frac{-5}{2})& =(\color{red}{a}+\color{orange}{(-8)}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(-8)} . \color{green}{(a)} + \color{orange}{(-8)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{2}a-8a+8.\frac{5}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{2})+(-8))a+\frac{40}{2} & \text{Neem samen} \\ &=a^2-\frac{21}{2}a+\frac{40}{2} & \text{Maak de som} \\ &=a^2-\frac{21}{2}a+20 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)