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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-10}{13})(\frac{4}{10}-a)& =(\color{red}{a}+\color{orange}{\frac{10}{13}}).(\color{green}{-a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{10}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{5}a-\frac{10}{13}a+\frac{10}{13}.\frac{2}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{5}+(\frac{-10}{13}))a+(\frac{-20}{65}) & \text{Neem samen} \\ &=-a^2-\frac{24}{65}a+(\frac{-20}{65}) & \text{Maak de som} \\ &=-a^2-\frac{24}{65}a+(\frac{-4}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(a+\frac{6}{2})(a+\frac{4}{20})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{5}a+3a+3.\frac{1}{5}& \text{Uitwerken } \\ & =a^2+(\frac{1}{5}+3)a+\frac{3}{5} & \text{Neem samen} \\ &=a^2+\frac{16}{5}a+\frac{3}{5} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-13}{11}+p)(x-\frac{18}{11})& =(\color{red}{p}+\color{orange}{\frac{-13}{11}}).(\color{green}{x}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{18}{11}p-\frac{13}{11}x+\frac{13}{11}.\frac{18}{11}& \text{Uitwerken } \\ & =px-\frac{18}{11}p-\frac{13}{11}x+\frac{234}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{13}{16}-a)(\frac{-5}{7}+p)& =(\color{red}{-a}+\color{orange}{\frac{13}{16}}).(\color{green}{p}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{13}{16})} . \color{green}{(p)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{7}a+\frac{13}{16}p-\frac{13}{16}.\frac{5}{7}& \text{Uitwerken } \\ & =-ap+\frac{5}{7}a+\frac{13}{16}p-\frac{65}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{2}+x)(\frac{-11}{7}+q)& =(\color{red}{x}+\color{orange}{9}).(\color{green}{q}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(9)} . \color{green}{(q)} + \color{orange}{(9)} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{7}x+9q-9.\frac{11}{7}& \text{Uitwerken } \\ & =qx-\frac{11}{7}x+9q-\frac{99}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{6}{6})(\frac{-15}{3}-q)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -pq-5p+1q+1.5& \text{Uitwerken } \\ & =-pq-5p+1q+5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{-12}{12})(\frac{-19}{11}-x)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{11}b+1x+1.\frac{19}{11}& \text{Uitwerken } \\ & =-bx-\frac{19}{11}b+1x+\frac{19}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{12}{6})(b-\frac{12}{3})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bq-4q-2b+2.4& \text{Uitwerken } \\ & =bq-4q-2b+8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{-17}{11})(b-(-17))& =(\color{red}{a}+\color{orange}{\frac{17}{11}}).(\color{green}{b}+\color{blue}{17})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(17)} + \color{orange}{(\frac{17}{11})} . \color{green}{(b)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = ab+17a+\frac{17}{11}b+\frac{17}{11}.17& \text{Uitwerken } \\ & =ab+17a+\frac{17}{11}b+\frac{289}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{19}{16}+a)(\frac{-10}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{19}{16}}).(\color{green}{q}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{19}{16})} . \color{green}{(q)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{17}a+\frac{19}{16}q-\frac{19}{16}.\frac{10}{17}& \text{Uitwerken } \\ & =aq-\frac{10}{17}a+\frac{19}{16}q-\frac{190}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{10}{17}a+\frac{19}{16}q-\frac{95}{136} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-9}{5}-p)(p-\frac{14}{14})& =(\color{red}{-p}+\color{orange}{\frac{-9}{5}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pp+1p-\frac{9}{5}p+\frac{9}{5}.1& \text{Uitwerken } \\ & =-p^2+(1+(\frac{-9}{5}))p+(\frac{-9}{5}) & \text{Neem samen} \\ &=-p^2-\frac{4}{5}p+(\frac{-9}{5}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(a+\frac{-9}{18})(\frac{-3}{6}+x)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a-\frac{1}{2}x+\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a-\frac{1}{2}x+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)