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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{17}{15}+a)(\frac{4}{2}+p)& =(\color{red}{a}+\color{orange}{\frac{17}{15}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{17}{15})} . \color{green}{(p)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a+\frac{17}{15}p+\frac{17}{15}.2& \text{Uitwerken } \\ & =ap+2a+\frac{17}{15}p+\frac{34}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-12}{3}+x)(\frac{2}{13}+x)& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{13}x-4x-4.\frac{2}{13}& \text{Uitwerken } \\ & =x^2+(\frac{2}{13}+(-4))x-(\frac{-8}{13}) & \text{Neem samen} \\ &=x^2-\frac{50}{13}x-(\frac{-8}{13}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(13-q)(\frac{-4}{16}-x)& =(\color{red}{-q}+\color{orange}{13}).(\color{green}{-x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(13)} . \color{green}{(-x)} + \color{orange}{(13)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}q-13x-13.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}q-13x-\frac{13}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{1}{7}-x)(a-\frac{-4}{12})& =(\color{red}{-x}+\color{orange}{\frac{1}{7}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{1}{7})} . \color{green}{(a)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{3}x+\frac{1}{7}a+\frac{1}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-ax-\frac{1}{3}x+\frac{1}{7}a+\frac{1}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{17}{13}+x)(\frac{-8}{4}+x)& =(\color{red}{x}+\color{orange}{\frac{17}{13}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{17}{13})} . \color{green}{(x)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = xx-2x+\frac{17}{13}x-\frac{17}{13}.2& \text{Uitwerken } \\ & =x^2+((-2)+\frac{17}{13})x-(\frac{-34}{13}) & \text{Neem samen} \\ &=x^2-\frac{9}{13}x-(\frac{-34}{13}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(q+\frac{20}{2})(\frac{9}{16}-a)& =(\color{red}{q}+\color{orange}{10}).(\color{green}{-a}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(10)} . \color{green}{(-a)} + \color{orange}{(10)} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{16}q-10a+10.\frac{9}{16}& \text{Uitwerken } \\ & =-aq+\frac{9}{16}q-10a+\frac{90}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{9}{16}q-10a+\frac{45}{8} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q-\frac{17}{17})(\frac{10}{6}+a)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{3}q-1a-1.\frac{5}{3}& \text{Uitwerken } \\ & =aq+\frac{5}{3}q-1a-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-18}{17}-p)(\frac{14}{3}-a)& =(\color{red}{-p}+\color{orange}{\frac{-18}{17}}).(\color{green}{-a}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{3}p+\frac{18}{17}a-\frac{18}{17}.\frac{14}{3}& \text{Uitwerken } \\ & =ap-\frac{14}{3}p+\frac{18}{17}a-\frac{252}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{14}{3}p+\frac{18}{17}a-\frac{84}{17} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a+\frac{-14}{14})(p-\frac{-12}{9})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}a-1p-1.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}a-1p-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-19}{20})(q-\frac{16}{20})& =(\color{red}{x}+\color{orange}{\frac{19}{20}}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{19}{20})} . \color{green}{(q)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{5}x+\frac{19}{20}q-\frac{19}{20}.\frac{4}{5}& \text{Uitwerken } \\ & =qx-\frac{4}{5}x+\frac{19}{20}q-\frac{76}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{4}{5}x+\frac{19}{20}q-\frac{19}{25} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{16}{3}+q)(\frac{-14}{15}+x)& =(\color{red}{q}+\color{orange}{\frac{16}{3}}).(\color{green}{x}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{16}{3})} . \color{green}{(x)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{15}q+\frac{16}{3}x-\frac{16}{3}.\frac{14}{15}& \text{Uitwerken } \\ & =qx-\frac{14}{15}q+\frac{16}{3}x-\frac{224}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{2}-b)(\frac{-19}{15}-p)& =(\color{red}{-b}+\color{orange}{\frac{-7}{2}}).(\color{green}{-p}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{15}b+\frac{7}{2}p+\frac{7}{2}.\frac{19}{15}& \text{Uitwerken } \\ & =bp+\frac{19}{15}b+\frac{7}{2}p+\frac{133}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)