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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{9}-a)(b-\frac{6}{4})& =(\color{red}{-a}+\color{orange}{\frac{-2}{9}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{2}a-\frac{2}{9}b+\frac{2}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =-ab+\frac{3}{2}a-\frac{2}{9}b+\frac{6}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{3}{2}a-\frac{2}{9}b+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-15}{6}+q)(b+\frac{-1}{18})& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{18}q-\frac{5}{2}b+\frac{5}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =bq-\frac{1}{18}q-\frac{5}{2}b+\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{18}{3})(a+\frac{10}{18})& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{9}x-6a-6.\frac{5}{9}& \text{Uitwerken } \\ & =ax+\frac{5}{9}x-6a-\frac{30}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{5}{9}x-6a-\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-14}{13}-a)(p+\frac{13}{9})& =(\color{red}{-a}+\color{orange}{\frac{-14}{13}}).(\color{green}{p}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{9}a-\frac{14}{13}p-\frac{14}{13}.\frac{13}{9}& \text{Uitwerken } \\ & =-ap-\frac{13}{9}a-\frac{14}{13}p-\frac{182}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{13}{9}a-\frac{14}{13}p-\frac{14}{9} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-20}{17}+x)(p+\frac{1}{4})& =(\color{red}{x}+\color{orange}{\frac{-20}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{4}x-\frac{20}{17}p-\frac{20}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =px+\frac{1}{4}x-\frac{20}{17}p-\frac{20}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{4}x-\frac{20}{17}p-\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p-\frac{-17}{2})(q+\frac{-6}{15})& =(\color{red}{p}+\color{orange}{\frac{17}{2}}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{17}{2})} . \color{green}{(q)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{5}p+\frac{17}{2}q-\frac{17}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =pq-\frac{2}{5}p+\frac{17}{2}q-\frac{34}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{5}p+\frac{17}{2}q-\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-10}{2}-b)(x+\frac{-13}{3})& =(\color{red}{-b}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{3}b-5x+5.\frac{13}{3}& \text{Uitwerken } \\ & =-bx+\frac{13}{3}b-5x+\frac{65}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{17}{18})(p+\frac{2}{8})& =(\color{red}{p}+\color{orange}{\frac{17}{18}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{17}{18})} . \color{green}{(p)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{4}p+\frac{17}{18}p+\frac{17}{18}.\frac{1}{4}& \text{Uitwerken } \\ & =p^2+(\frac{1}{4}+\frac{17}{18})p+\frac{17}{72} & \text{Neem samen} \\ &=p^2+\frac{43}{36}p+\frac{17}{72} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}((-12)-a)(p-\frac{13}{14})& =(\color{red}{-a}+\color{orange}{(-12)}).(\color{green}{p}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(-12)} . \color{green}{(p)} + \color{orange}{(-12)} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{14}a-12p+12.\frac{13}{14}& \text{Uitwerken } \\ & =-ap+\frac{13}{14}a-12p+\frac{156}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{13}{14}a-12p+\frac{78}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(b-\frac{-12}{3})(\frac{-16}{11}-p)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{-p}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(4)} . \color{green}{(-p)} + \color{orange}{(4)} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{16}{11}b-4p-4.\frac{16}{11}& \text{Uitwerken } \\ & =-bp-\frac{16}{11}b-4p-\frac{64}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{2}{13})(b+\frac{20}{6})& =(\color{red}{p}+\color{orange}{\frac{-2}{13}}).(\color{green}{b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{10}{3}p-\frac{2}{13}b-\frac{2}{13}.\frac{10}{3}& \text{Uitwerken } \\ & =bp+\frac{10}{3}p-\frac{2}{13}b-\frac{20}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-13}{13}-a)(q-\frac{1}{19})& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{19}a-1q+1.\frac{1}{19}& \text{Uitwerken } \\ & =-aq+\frac{1}{19}a-1q+\frac{1}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)