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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-16}{4})(p+\frac{-8}{9})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{9}p-4p+4.\frac{8}{9}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{9})+(-4))p+\frac{32}{9} & \text{Neem samen} \\ &=p^2-\frac{44}{9}p+\frac{32}{9} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(b-\frac{16}{19})(\frac{-6}{2}+p)& =(\color{red}{b}+\color{orange}{\frac{-16}{19}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp-3b-\frac{16}{19}p+\frac{16}{19}.3& \text{Uitwerken } \\ & =bp-3b-\frac{16}{19}p+\frac{48}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{8}{2})(a+14)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{a}+\color{blue}{14})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(14)} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = aa+14a+4a+4.14& \text{Uitwerken } \\ & =a^2+(14+4)a+56 & \text{Neem samen} \\ &=a^2+18a+56 & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(b+\frac{13}{11})(p+\frac{-20}{17})& =(\color{red}{b}+\color{orange}{\frac{13}{11}}).(\color{green}{p}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{13}{11})} . \color{green}{(p)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{20}{17}b+\frac{13}{11}p-\frac{13}{11}.\frac{20}{17}& \text{Uitwerken } \\ & =bp-\frac{20}{17}b+\frac{13}{11}p-\frac{260}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{1}{15}-q)(p-\frac{-1}{6})& =(\color{red}{-q}+\color{orange}{\frac{1}{15}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{1}{15})} . \color{green}{(p)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{6}q+\frac{1}{15}p+\frac{1}{15}.\frac{1}{6}& \text{Uitwerken } \\ & =-pq-\frac{1}{6}q+\frac{1}{15}p+\frac{1}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-6}{6}+p)(\frac{20}{19}-a)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{20}{19}p+1a-1.\frac{20}{19}& \text{Uitwerken } \\ & =-ap+\frac{20}{19}p+1a-\frac{20}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{2}+q)(x+\frac{-9}{20})& =(\color{red}{q}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{20}q+\frac{7}{2}x-\frac{7}{2}.\frac{9}{20}& \text{Uitwerken } \\ & =qx-\frac{9}{20}q+\frac{7}{2}x-\frac{63}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{-4}{3})(\frac{3}{9}+q)& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}b+\frac{4}{3}q+\frac{4}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}b+\frac{4}{3}q+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{2}{5})(\frac{-11}{10}-a)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{-a}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{10}x-\frac{2}{5}a-\frac{2}{5}.\frac{11}{10}& \text{Uitwerken } \\ & =-ax-\frac{11}{10}x-\frac{2}{5}a-\frac{22}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{11}{10}x-\frac{2}{5}a-\frac{11}{25} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-6}{13}+x)(\frac{-16}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{-6}{13}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-6}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x-\frac{6}{13}a+\frac{6}{13}.1& \text{Uitwerken } \\ & =ax-1x-\frac{6}{13}a+\frac{6}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{16}{6}+b)(x+\frac{8}{16})& =(\color{red}{b}+\color{orange}{\frac{8}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}b+\frac{8}{3}x+\frac{8}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}b+\frac{8}{3}x+\frac{8}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{1}{2}b+\frac{8}{3}x+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{11}+x)(\frac{16}{15}-p)& =(\color{red}{x}+\color{orange}{\frac{-7}{11}}).(\color{green}{-p}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{16}{15}x+\frac{7}{11}p-\frac{7}{11}.\frac{16}{15}& \text{Uitwerken } \\ & =-px+\frac{16}{15}x+\frac{7}{11}p-\frac{112}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)