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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}((-7)+b)(x-9)& =(\color{red}{b}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = bx-9b-7x+7.9& \text{Uitwerken } \\ & =bx-9b-7x+63 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{13}+p)(\frac{15}{7}+p)& =(\color{red}{p}+\color{orange}{\frac{-9}{13}}).(\color{green}{p}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{15}{7}p-\frac{9}{13}p-\frac{9}{13}.\frac{15}{7}& \text{Uitwerken } \\ & =p^2+(\frac{15}{7}+(\frac{-9}{13}))p-(\frac{-135}{91}) & \text{Neem samen} \\ &=p^2+\frac{132}{91}p-(\frac{-135}{91}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(q-\frac{-15}{6})(\frac{-13}{5}-a)& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{-a}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{5}q-\frac{5}{2}a-\frac{5}{2}.\frac{13}{5}& \text{Uitwerken } \\ & =-aq-\frac{13}{5}q-\frac{5}{2}a-\frac{65}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{13}{5}q-\frac{5}{2}a-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{13}{19}+q)(\frac{6}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{13}{19}}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{13}{19})} . \color{green}{(x)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{3}q+\frac{13}{19}x+\frac{13}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =qx+\frac{1}{3}q+\frac{13}{19}x+\frac{13}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{19}{15}+a)(\frac{7}{2}+x)& =(\color{red}{a}+\color{orange}{\frac{19}{15}}).(\color{green}{x}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{19}{15})} . \color{green}{(x)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{2}a+\frac{19}{15}x+\frac{19}{15}.\frac{7}{2}& \text{Uitwerken } \\ & =ax+\frac{7}{2}a+\frac{19}{15}x+\frac{133}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{3}{12})(\frac{-5}{6}+a)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{6}b+\frac{1}{4}a-\frac{1}{4}.\frac{5}{6}& \text{Uitwerken } \\ & =ab-\frac{5}{6}b+\frac{1}{4}a-\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{8}{4})(q-\frac{-19}{14})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{14}x+2q+2.\frac{19}{14}& \text{Uitwerken } \\ & =qx+\frac{19}{14}x+2q+\frac{38}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{19}{14}x+2q+\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{-16}{7})(\frac{8}{17}-x)& =(\color{red}{q}+\color{orange}{\frac{16}{7}}).(\color{green}{-x}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{16}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{8}{17}q-\frac{16}{7}x+\frac{16}{7}.\frac{8}{17}& \text{Uitwerken } \\ & =-qx+\frac{8}{17}q-\frac{16}{7}x+\frac{128}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-16}{12}-x)(b-\frac{2}{7})& =(\color{red}{-x}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{2}{7}x-\frac{4}{3}b+\frac{4}{3}.\frac{2}{7}& \text{Uitwerken } \\ & =-bx+\frac{2}{7}x-\frac{4}{3}b+\frac{8}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{16}{7}-x)(p+\frac{7}{4})& =(\color{red}{-x}+\color{orange}{\frac{16}{7}}).(\color{green}{p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{16}{7})} . \color{green}{(p)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{4}x+\frac{16}{7}p+\frac{16}{7}.\frac{7}{4}& \text{Uitwerken } \\ & =-px-\frac{7}{4}x+\frac{16}{7}p+\frac{112}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{7}{4}x+\frac{16}{7}p+4 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x+\frac{-3}{5})(\frac{19}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{3}x-\frac{3}{5}q-\frac{3}{5}.\frac{19}{3}& \text{Uitwerken } \\ & =qx+\frac{19}{3}x-\frac{3}{5}q-\frac{57}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{19}{3}x-\frac{3}{5}q-\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a-\frac{18}{7})(\frac{2}{8}-b)& =(\color{red}{a}+\color{orange}{\frac{-18}{7}}).(\color{green}{-b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{4}a+\frac{18}{7}b-\frac{18}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =-ab+\frac{1}{4}a+\frac{18}{7}b-\frac{18}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{1}{4}a+\frac{18}{7}b-\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)