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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{3}+b)(\frac{-4}{17}-a)& =(\color{red}{b}+\color{orange}{\frac{-10}{3}}).(\color{green}{-a}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{17}b+\frac{10}{3}a+\frac{10}{3}.\frac{4}{17}& \text{Uitwerken } \\ & =-ab-\frac{4}{17}b+\frac{10}{3}a+\frac{40}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-16}{8}-b)(q+\frac{11}{7})& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{7}b-2q-2.\frac{11}{7}& \text{Uitwerken } \\ & =-bq-\frac{11}{7}b-2q-\frac{22}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-5}{3}-a)(\frac{12}{9}+x)& =(\color{red}{-a}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{3}a-\frac{5}{3}x-\frac{5}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =-ax-\frac{4}{3}a-\frac{5}{3}x-\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-5}{14}-a)(\frac{9}{5}+p)& =(\color{red}{-a}+\color{orange}{\frac{-5}{14}}).(\color{green}{p}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{5}a-\frac{5}{14}p-\frac{5}{14}.\frac{9}{5}& \text{Uitwerken } \\ & =-ap-\frac{9}{5}a-\frac{5}{14}p-\frac{45}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{9}{5}a-\frac{5}{14}p-\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{11}{4}-a)(\frac{-16}{5}+q)& =(\color{red}{-a}+\color{orange}{\frac{11}{4}}).(\color{green}{q}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{11}{4})} . \color{green}{(q)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{16}{5}a+\frac{11}{4}q-\frac{11}{4}.\frac{16}{5}& \text{Uitwerken } \\ & =-aq+\frac{16}{5}a+\frac{11}{4}q-\frac{176}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{16}{5}a+\frac{11}{4}q-\frac{44}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(3-p)(\frac{-11}{17}-q)& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{-q}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(3)} . \color{green}{(-q)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{17}p-3q-3.\frac{11}{17}& \text{Uitwerken } \\ & =pq+\frac{11}{17}p-3q-\frac{33}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{18}{14}+q)(\frac{-20}{20}-q)& =(\color{red}{q}+\color{orange}{\frac{9}{7}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{9}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q-\frac{9}{7}q-\frac{9}{7}.1& \text{Uitwerken } \\ & =-q^2+((-1)+(\frac{-9}{7}))q-\frac{9}{7} & \text{Neem samen} \\ &=-q^2-\frac{16}{7}q-\frac{9}{7} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{2}{18}+a)(\frac{4}{7}+a)& =(\color{red}{a}+\color{orange}{\frac{1}{9}}).(\color{green}{a}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{7}a+\frac{1}{9}a+\frac{1}{9}.\frac{4}{7}& \text{Uitwerken } \\ & =a^2+(\frac{4}{7}+\frac{1}{9})a+\frac{4}{63} & \text{Neem samen} \\ &=a^2+\frac{43}{63}a+\frac{4}{63} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(x+\frac{16}{9})(p+(-16))& =(\color{red}{x}+\color{orange}{\frac{16}{9}}).(\color{green}{p}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-16)} + \color{orange}{(\frac{16}{9})} . \color{green}{(p)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = px-16x+\frac{16}{9}p-\frac{16}{9}.16& \text{Uitwerken } \\ & =px-16x+\frac{16}{9}p-\frac{256}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-11}{5}+p)(x+\frac{8}{18})& =(\color{red}{p}+\color{orange}{\frac{-11}{5}}).(\color{green}{x}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{9}p-\frac{11}{5}x-\frac{11}{5}.\frac{4}{9}& \text{Uitwerken } \\ & =px+\frac{4}{9}p-\frac{11}{5}x-\frac{44}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{16}{20})(\frac{19}{10}-a)& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{-a}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{10}p+\frac{4}{5}a-\frac{4}{5}.\frac{19}{10}& \text{Uitwerken } \\ & =-ap+\frac{19}{10}p+\frac{4}{5}a-\frac{76}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{19}{10}p+\frac{4}{5}a-\frac{38}{25} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(p-\frac{-6}{18})(q-\frac{6}{3})& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p+\frac{1}{3}q-\frac{1}{3}.2& \text{Uitwerken } \\ & =pq-2p+\frac{1}{3}q-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)