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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{15}{14})(\frac{6}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{-15}{14}}).(\color{green}{a}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{8}b-\frac{15}{14}a-\frac{15}{14}.\frac{3}{8}& \text{Uitwerken } \\ & =ab+\frac{3}{8}b-\frac{15}{14}a-\frac{45}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-10}{17}-b)(p-\frac{13}{7})& =(\color{red}{-b}+\color{orange}{\frac{-10}{17}}).(\color{green}{p}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{7}b-\frac{10}{17}p+\frac{10}{17}.\frac{13}{7}& \text{Uitwerken } \\ & =-bp+\frac{13}{7}b-\frac{10}{17}p+\frac{130}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{12}{4}-a)(p+\frac{7}{11})& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{11}a+3p+3.\frac{7}{11}& \text{Uitwerken } \\ & =-ap-\frac{7}{11}a+3p+\frac{21}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-1}{10}+q)(x-\frac{9}{8})& =(\color{red}{q}+\color{orange}{\frac{-1}{10}}).(\color{green}{x}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{8}q-\frac{1}{10}x+\frac{1}{10}.\frac{9}{8}& \text{Uitwerken } \\ & =qx-\frac{9}{8}q-\frac{1}{10}x+\frac{9}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a+\frac{16}{5})(b-(-2))& =(\color{red}{a}+\color{orange}{\frac{16}{5}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{16}{5})} . \color{green}{(b)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2a+\frac{16}{5}b+\frac{16}{5}.2& \text{Uitwerken } \\ & =ab+2a+\frac{16}{5}b+\frac{32}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{19}{17})(q-\frac{4}{9})& =(\color{red}{a}+\color{orange}{\frac{19}{17}}).(\color{green}{q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{19}{17})} . \color{green}{(q)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{9}a+\frac{19}{17}q-\frac{19}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =aq-\frac{4}{9}a+\frac{19}{17}q-\frac{76}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{5}{3}-b)(\frac{15}{16}-p)& =(\color{red}{-b}+\color{orange}{\frac{5}{3}}).(\color{green}{-p}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{15}{16}b-\frac{5}{3}p+\frac{5}{3}.\frac{15}{16}& \text{Uitwerken } \\ & =bp-\frac{15}{16}b-\frac{5}{3}p+\frac{75}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{15}{16}b-\frac{5}{3}p+\frac{25}{16} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a+\frac{10}{11})(\frac{6}{2}-q)& =(\color{red}{a}+\color{orange}{\frac{10}{11}}).(\color{green}{-q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{10}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -aq+3a-\frac{10}{11}q+\frac{10}{11}.3& \text{Uitwerken } \\ & =-aq+3a-\frac{10}{11}q+\frac{30}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+(-7))(x+\frac{-13}{17})& =(\color{red}{p}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{17}p-7x+7.\frac{13}{17}& \text{Uitwerken } \\ & =px-\frac{13}{17}p-7x+\frac{91}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-9}{2})(q-\frac{15}{8})& =(\color{red}{a}+\color{orange}{\frac{-9}{2}}).(\color{green}{q}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{8}a-\frac{9}{2}q+\frac{9}{2}.\frac{15}{8}& \text{Uitwerken } \\ & =aq-\frac{15}{8}a-\frac{9}{2}q+\frac{135}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{15}{2})(p+(-11))& =(\color{red}{p}+\color{orange}{\frac{-15}{2}}).(\color{green}{p}+\color{blue}{(-11)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-11)} + \color{orange}{(\frac{-15}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = pp-11p-\frac{15}{2}p+\frac{15}{2}.11& \text{Uitwerken } \\ & =p^2+((-11)+(\frac{-15}{2}))p+\frac{165}{2} & \text{Neem samen} \\ &=p^2-\frac{37}{2}p+\frac{165}{2} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(b-\frac{-12}{11})(\frac{4}{13}+q)& =(\color{red}{b}+\color{orange}{\frac{12}{11}}).(\color{green}{q}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{13}b+\frac{12}{11}q+\frac{12}{11}.\frac{4}{13}& \text{Uitwerken } \\ & =bq+\frac{4}{13}b+\frac{12}{11}q+\frac{48}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)