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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-11}{11})(\frac{-10}{16}+b)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{8}a-1b+1.\frac{5}{8}& \text{Uitwerken } \\ & =ab-\frac{5}{8}a-1b+\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{19}-a)(\frac{15}{8}+x)& =(\color{red}{-a}+\color{orange}{\frac{8}{19}}).(\color{green}{x}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{8}{19})} . \color{green}{(x)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{8}a+\frac{8}{19}x+\frac{8}{19}.\frac{15}{8}& \text{Uitwerken } \\ & =-ax-\frac{15}{8}a+\frac{8}{19}x+\frac{120}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{15}{8}a+\frac{8}{19}x+\frac{15}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-6}{3})(p-\frac{-7}{17})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{17}b+2p+2.\frac{7}{17}& \text{Uitwerken } \\ & =bp+\frac{7}{17}b+2p+\frac{14}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}((-20)+p)(b-\frac{4}{13})& =(\color{red}{p}+\color{orange}{(-20)}).(\color{green}{b}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(-20)} . \color{green}{(b)} + \color{orange}{(-20)} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{13}p-20b+20.\frac{4}{13}& \text{Uitwerken } \\ & =bp-\frac{4}{13}p-20b+\frac{80}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{16}-b)(x+\frac{-7}{11})& =(\color{red}{-b}+\color{orange}{\frac{-1}{16}}).(\color{green}{x}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{11}b-\frac{1}{16}x+\frac{1}{16}.\frac{7}{11}& \text{Uitwerken } \\ & =-bx+\frac{7}{11}b-\frac{1}{16}x+\frac{7}{176} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-6}{7})(q-\frac{-3}{4})& =(\color{red}{a}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{4}a-\frac{6}{7}q-\frac{6}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =aq+\frac{3}{4}a-\frac{6}{7}q-\frac{18}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{4}a-\frac{6}{7}q-\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-18}{13})(\frac{20}{12}+q)& =(\color{red}{p}+\color{orange}{\frac{-18}{13}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{3}p-\frac{18}{13}q-\frac{18}{13}.\frac{5}{3}& \text{Uitwerken } \\ & =pq+\frac{5}{3}p-\frac{18}{13}q-\frac{90}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{3}p-\frac{18}{13}q-\frac{30}{13} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{12}-b)(\frac{6}{17}-q)& =(\color{red}{-b}+\color{orange}{\frac{1}{12}}).(\color{green}{-q}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{1}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{6}{17}b-\frac{1}{12}q+\frac{1}{12}.\frac{6}{17}& \text{Uitwerken } \\ & =bq-\frac{6}{17}b-\frac{1}{12}q+\frac{6}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{6}{17}b-\frac{1}{12}q+\frac{1}{34} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{10}{2})(\frac{-17}{19}-p)& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{-p}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(-5)} . \color{green}{(-p)} + \color{orange}{(-5)} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{19}x+5p+5.\frac{17}{19}& \text{Uitwerken } \\ & =-px-\frac{17}{19}x+5p+\frac{85}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{5}-q)(\frac{10}{20}-q)& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{2}q-2q+2.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{2})+(-2))q+\frac{2}{2} & \text{Neem samen} \\ &=q^2-\frac{5}{2}q+\frac{2}{2} & \text{Maak de som} \\ &=q^2-\frac{5}{2}q+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{9}{3}-p)(p-\frac{16}{14})& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{8}{7}p+3p-3.\frac{8}{7}& \text{Uitwerken } \\ & =-p^2+(\frac{8}{7}+3)p-\frac{24}{7} & \text{Neem samen} \\ &=-p^2+\frac{29}{7}p-\frac{24}{7} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-4}{2}+p)(8-p)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{8})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(8)} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -pp+8p+2p-2.8& \text{Uitwerken } \\ & =-p^2+(8+2)p-16 & \text{Neem samen} \\ &=-p^2+10p-16 & \text{Maak de som} \\\end{align}\)
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