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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{7}{16})(a-\frac{20}{4})& =(\color{red}{x}+\color{orange}{\frac{7}{16}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(\frac{7}{16})} . \color{green}{(a)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ax-5x+\frac{7}{16}a-\frac{7}{16}.5& \text{Uitwerken } \\ & =ax-5x+\frac{7}{16}a-\frac{35}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{10}{14})(\frac{-5}{14}-b)& =(\color{red}{a}+\color{orange}{\frac{5}{7}}).(\color{green}{-b}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{5}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{14}a-\frac{5}{7}b-\frac{5}{7}.\frac{5}{14}& \text{Uitwerken } \\ & =-ab-\frac{5}{14}a-\frac{5}{7}b-\frac{25}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{11}{9}+q)(a-\frac{3}{3})& =(\color{red}{q}+\color{orange}{\frac{11}{9}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1q+\frac{11}{9}a-\frac{11}{9}.1& \text{Uitwerken } \\ & =aq-1q+\frac{11}{9}a-\frac{11}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{18}{5})(q+\frac{-2}{10})& =(\color{red}{a}+\color{orange}{\frac{18}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{18}{5})} . \color{green}{(q)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{5}a+\frac{18}{5}q-\frac{18}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =aq-\frac{1}{5}a+\frac{18}{5}q-\frac{18}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{-12}{15})(a+\frac{-5}{17})& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{17}b-\frac{4}{5}a+\frac{4}{5}.\frac{5}{17}& \text{Uitwerken } \\ & =ab-\frac{5}{17}b-\frac{4}{5}a+\frac{20}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{17}b-\frac{4}{5}a+\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-9}{20}-x)(\frac{13}{8}-x)& =(\color{red}{-x}+\color{orange}{\frac{-9}{20}}).(\color{green}{-x}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{13}{8}x+\frac{9}{20}x-\frac{9}{20}.\frac{13}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-13}{8})+\frac{9}{20})x-(\frac{-117}{160}) & \text{Neem samen} \\ &=x^2-\frac{47}{40}x-(\frac{-117}{160}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(10-p)(\frac{18}{6}-x)& =(\color{red}{-p}+\color{orange}{10}).(\color{green}{-x}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(3)} + \color{orange}{(10)} . \color{green}{(-x)} + \color{orange}{(10)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = px-3p-10x+10.3& \text{Uitwerken } \\ & =px-3p-10x+30 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-2}{20}-a)(\frac{15}{13}-x)& =(\color{red}{-a}+\color{orange}{\frac{-1}{10}}).(\color{green}{-x}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{13}a+\frac{1}{10}x-\frac{1}{10}.\frac{15}{13}& \text{Uitwerken } \\ & =ax-\frac{15}{13}a+\frac{1}{10}x-\frac{15}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{15}{13}a+\frac{1}{10}x-\frac{3}{26} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{10}{12}-p)(\frac{13}{8}+x)& =(\color{red}{-p}+\color{orange}{\frac{5}{6}}).(\color{green}{x}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{8}p+\frac{5}{6}x+\frac{5}{6}.\frac{13}{8}& \text{Uitwerken } \\ & =-px-\frac{13}{8}p+\frac{5}{6}x+\frac{65}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{-9}{10})(b-(-16))& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{16})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(16)} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = bq+16q+\frac{9}{10}b+\frac{9}{10}.16& \text{Uitwerken } \\ & =bq+16q+\frac{9}{10}b+\frac{144}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+16q+\frac{9}{10}b+\frac{72}{5} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{16}{18}+b)(\frac{1}{19}+a)& =(\color{red}{b}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{19}b+\frac{8}{9}a+\frac{8}{9}.\frac{1}{19}& \text{Uitwerken } \\ & =ab+\frac{1}{19}b+\frac{8}{9}a+\frac{8}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-17}{13}+b)(b-\frac{5}{17})& =(\color{red}{b}+\color{orange}{\frac{-17}{13}}).(\color{green}{b}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{17}b-\frac{17}{13}b+\frac{17}{13}.\frac{5}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{17})+(\frac{-17}{13}))b+\frac{85}{221} & \text{Neem samen} \\ &=b^2-\frac{354}{221}b+\frac{85}{221} & \text{Maak de som} \\ &=b^2-\frac{354}{221}b+\frac{5}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)