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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{12}{19})(\frac{-7}{19}+q)& =(\color{red}{q}+\color{orange}{\frac{-12}{19}}).(\color{green}{q}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{19}q-\frac{12}{19}q+\frac{12}{19}.\frac{7}{19}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{19})+(\frac{-12}{19}))q+\frac{84}{361} & \text{Neem samen} \\ &=q^2-\frac{19}{19}q+\frac{84}{361} & \text{Maak de som} \\ &=q^2-1q+\frac{84}{361} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(b-\frac{-5}{16})(14-q)& =(\color{red}{b}+\color{orange}{\frac{5}{16}}).(\color{green}{-q}+\color{blue}{14})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(14)} + \color{orange}{(\frac{5}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = -bq+14b-\frac{5}{16}q+\frac{5}{16}.14& \text{Uitwerken } \\ & =-bq+14b-\frac{5}{16}q+\frac{70}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+14b-\frac{5}{16}q+\frac{35}{8} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}((-7)+q)(x-\frac{-7}{2})& =(\color{red}{q}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{2}q-7x-7.\frac{7}{2}& \text{Uitwerken } \\ & =qx+\frac{7}{2}q-7x-\frac{49}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{11}{20})(\frac{-1}{4}-x)& =(\color{red}{p}+\color{orange}{\frac{11}{20}}).(\color{green}{-x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{11}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{4}p-\frac{11}{20}x-\frac{11}{20}.\frac{1}{4}& \text{Uitwerken } \\ & =-px-\frac{1}{4}p-\frac{11}{20}x-\frac{11}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{16}{3})(\frac{16}{8}-p)& =(\color{red}{b}+\color{orange}{\frac{-16}{3}}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-16}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2b+\frac{16}{3}p-\frac{16}{3}.2& \text{Uitwerken } \\ & =-bp+2b+\frac{16}{3}p-\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{20}{6}-q)(\frac{13}{6}+x)& =(\color{red}{-q}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{6}q+\frac{10}{3}x+\frac{10}{3}.\frac{13}{6}& \text{Uitwerken } \\ & =-qx-\frac{13}{6}q+\frac{10}{3}x+\frac{130}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{13}{6}q+\frac{10}{3}x+\frac{65}{9} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{-2}{2})(\frac{-4}{12}-b)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{3}b-1b-1.\frac{1}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{3})+(-1))b-\frac{1}{3} & \text{Neem samen} \\ &=-b^2-\frac{4}{3}b-\frac{1}{3} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(x+(-11))(a-\frac{-6}{5})& =(\color{red}{x}+\color{orange}{(-11)}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(-11)} . \color{green}{(a)} + \color{orange}{(-11)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{5}x-11a-11.\frac{6}{5}& \text{Uitwerken } \\ & =ax+\frac{6}{5}x-11a-\frac{66}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{15}{4}-x)(a-\frac{1}{16})& =(\color{red}{-x}+\color{orange}{\frac{15}{4}}).(\color{green}{a}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{15}{4})} . \color{green}{(a)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{16}x+\frac{15}{4}a-\frac{15}{4}.\frac{1}{16}& \text{Uitwerken } \\ & =-ax+\frac{1}{16}x+\frac{15}{4}a-\frac{15}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{19}{14}-p)(b-\frac{15}{20})& =(\color{red}{-p}+\color{orange}{\frac{19}{14}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{19}{14})} . \color{green}{(b)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{4}p+\frac{19}{14}b-\frac{19}{14}.\frac{3}{4}& \text{Uitwerken } \\ & =-bp+\frac{3}{4}p+\frac{19}{14}b-\frac{57}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-7}{2})(\frac{13}{4}+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{p}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{4}p-\frac{7}{2}p-\frac{7}{2}.\frac{13}{4}& \text{Uitwerken } \\ & =p^2+(\frac{13}{4}+(\frac{-7}{2}))p-(\frac{-91}{8}) & \text{Neem samen} \\ &=p^2-\frac{1}{4}p-(\frac{-91}{8}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p+\frac{5}{4})(a+\frac{-7}{3})& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{3}p+\frac{5}{4}a-\frac{5}{4}.\frac{7}{3}& \text{Uitwerken } \\ & =ap-\frac{7}{3}p+\frac{5}{4}a-\frac{35}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)