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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{3}+b)(p-\frac{4}{19})& =(\color{red}{b}+\color{orange}{\frac{16}{3}}).(\color{green}{p}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{16}{3})} . \color{green}{(p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{19}b+\frac{16}{3}p-\frac{16}{3}.\frac{4}{19}& \text{Uitwerken } \\ & =bp-\frac{4}{19}b+\frac{16}{3}p-\frac{64}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-12}{12}-b)(\frac{16}{11}+q)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{11}b-1q-1.\frac{16}{11}& \text{Uitwerken } \\ & =-bq-\frac{16}{11}b-1q-\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-19}{11}-p)(\frac{15}{12}-b)& =(\color{red}{-p}+\color{orange}{\frac{-19}{11}}).(\color{green}{-b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{4}p+\frac{19}{11}b-\frac{19}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =bp-\frac{5}{4}p+\frac{19}{11}b-\frac{95}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{12}{5}-x)(p-\frac{-9}{12})& =(\color{red}{-x}+\color{orange}{\frac{12}{5}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{12}{5})} . \color{green}{(p)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{4}x+\frac{12}{5}p+\frac{12}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =-px-\frac{3}{4}x+\frac{12}{5}p+\frac{36}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{3}{4}x+\frac{12}{5}p+\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-14}{8}-b)(q-\frac{-17}{20})& =(\color{red}{-b}+\color{orange}{\frac{-7}{4}}).(\color{green}{q}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{17}{20}b-\frac{7}{4}q-\frac{7}{4}.\frac{17}{20}& \text{Uitwerken } \\ & =-bq-\frac{17}{20}b-\frac{7}{4}q-\frac{119}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{3}{10})(\frac{20}{6}-b)& =(\color{red}{a}+\color{orange}{\frac{3}{10}}).(\color{green}{-b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{3}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{10}{3}a-\frac{3}{10}b+\frac{3}{10}.\frac{10}{3}& \text{Uitwerken } \\ & =-ab+\frac{10}{3}a-\frac{3}{10}b+\frac{30}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{10}{3}a-\frac{3}{10}b+1 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(a-\frac{-12}{4})(\frac{19}{7}-b)& =(\color{red}{a}+\color{orange}{3}).(\color{green}{-b}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(3)} . \color{green}{(-b)} + \color{orange}{(3)} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{7}a-3b+3.\frac{19}{7}& \text{Uitwerken } \\ & =-ab+\frac{19}{7}a-3b+\frac{57}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{-7}{14})(\frac{-16}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{9}q+\frac{1}{2}x-\frac{1}{2}.\frac{8}{9}& \text{Uitwerken } \\ & =qx-\frac{8}{9}q+\frac{1}{2}x-\frac{8}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{8}{9}q+\frac{1}{2}x-\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q+\frac{-8}{4})(\frac{9}{2}+x)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{2}q-2x-2.\frac{9}{2}& \text{Uitwerken } \\ & =qx+\frac{9}{2}q-2x-\frac{18}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{9}{2}q-2x-9 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{14}{19})(\frac{-13}{11}+q)& =(\color{red}{p}+\color{orange}{\frac{14}{19}}).(\color{green}{q}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{14}{19})} . \color{green}{(q)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{11}p+\frac{14}{19}q-\frac{14}{19}.\frac{13}{11}& \text{Uitwerken } \\ & =pq-\frac{13}{11}p+\frac{14}{19}q-\frac{182}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-1}{19}+q)(\frac{2}{12}+x)& =(\color{red}{q}+\color{orange}{\frac{-1}{19}}).(\color{green}{x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{6}q-\frac{1}{19}x-\frac{1}{19}.\frac{1}{6}& \text{Uitwerken } \\ & =qx+\frac{1}{6}q-\frac{1}{19}x-\frac{1}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{7}+a)(a-\frac{-16}{8})& =(\color{red}{a}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aa+2a-\frac{5}{7}a-\frac{5}{7}.2& \text{Uitwerken } \\ & =a^2+(2+(\frac{-5}{7}))a-(\frac{-10}{7}) & \text{Neem samen} \\ &=a^2+\frac{9}{7}a-(\frac{-10}{7}) & \text{Maak de som} \\\end{align}\)