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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-16}{18}+q)(x-8)& =(\color{red}{q}+\color{orange}{\frac{-8}{9}}).(\color{green}{x}+\color{blue}{(-8)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-8)} + \color{orange}{(\frac{-8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = qx-8q-\frac{8}{9}x+\frac{8}{9}.8& \text{Uitwerken } \\ & =qx-8q-\frac{8}{9}x+\frac{64}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-4}{6})(a+\frac{-18}{14})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{7}b+\frac{2}{3}a-\frac{2}{3}.\frac{9}{7}& \text{Uitwerken } \\ & =ab-\frac{9}{7}b+\frac{2}{3}a-\frac{18}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{7}b+\frac{2}{3}a-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{-14}{9})(\frac{1}{7}-a)& =(\color{red}{x}+\color{orange}{\frac{14}{9}}).(\color{green}{-a}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{14}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{7}x-\frac{14}{9}a+\frac{14}{9}.\frac{1}{7}& \text{Uitwerken } \\ & =-ax+\frac{1}{7}x-\frac{14}{9}a+\frac{14}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{1}{7}x-\frac{14}{9}a+\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-18}{10}-x)(q+\frac{17}{18})& =(\color{red}{-x}+\color{orange}{\frac{-9}{5}}).(\color{green}{q}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{18}x-\frac{9}{5}q-\frac{9}{5}.\frac{17}{18}& \text{Uitwerken } \\ & =-qx-\frac{17}{18}x-\frac{9}{5}q-\frac{153}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{17}{18}x-\frac{9}{5}q-\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{-15}{9})(\frac{-6}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ax-3x-\frac{5}{3}a+\frac{5}{3}.3& \text{Uitwerken } \\ & =ax-3x-\frac{5}{3}a+\frac{15}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-3x-\frac{5}{3}a+5 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{10}-b)(\frac{13}{16}+p)& =(\color{red}{-b}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{16}b-\frac{7}{10}p-\frac{7}{10}.\frac{13}{16}& \text{Uitwerken } \\ & =-bp-\frac{13}{16}b-\frac{7}{10}p-\frac{91}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{12}{18}-b)(b-\frac{2}{7})& =(\color{red}{-b}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{2}{7}b+\frac{2}{3}b-\frac{2}{3}.\frac{2}{7}& \text{Uitwerken } \\ & =-b^2+(\frac{2}{7}+\frac{2}{3})b-\frac{4}{21} & \text{Neem samen} \\ &=-b^2+\frac{20}{21}b-\frac{4}{21} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-10}{4}-x)(b+\frac{-5}{11})& =(\color{red}{-x}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{11}x-\frac{5}{2}b+\frac{5}{2}.\frac{5}{11}& \text{Uitwerken } \\ & =-bx+\frac{5}{11}x-\frac{5}{2}b+\frac{25}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a+\frac{-7}{16})(\frac{8}{9}-x)& =(\color{red}{a}+\color{orange}{\frac{-7}{16}}).(\color{green}{-x}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{8}{9}a+\frac{7}{16}x-\frac{7}{16}.\frac{8}{9}& \text{Uitwerken } \\ & =-ax+\frac{8}{9}a+\frac{7}{16}x-\frac{56}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{8}{9}a+\frac{7}{16}x-\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(4-x)(x-\frac{-17}{2})& =(\color{red}{-x}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{17}{2}x+4x+4.\frac{17}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-17}{2})+4)x+(\frac{-68}{2}) & \text{Neem samen} \\ &=-x^2-\frac{9}{2}x+(\frac{-68}{2}) & \text{Maak de som} \\ &=-x^2-\frac{9}{2}x+(-34) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(b-\frac{-1}{5})(a+\frac{-14}{11})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{14}{11}b+\frac{1}{5}a-\frac{1}{5}.\frac{14}{11}& \text{Uitwerken } \\ & =ab-\frac{14}{11}b+\frac{1}{5}a-\frac{14}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{1}{7}-a)(q+\frac{5}{17})& =(\color{red}{-a}+\color{orange}{\frac{1}{7}}).(\color{green}{q}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{17}a+\frac{1}{7}q+\frac{1}{7}.\frac{5}{17}& \text{Uitwerken } \\ & =-aq-\frac{5}{17}a+\frac{1}{7}q+\frac{5}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)