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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(11+a)(p-\frac{12}{2})& =(\color{red}{a}+\color{orange}{11}).(\color{green}{p}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-6)} + \color{orange}{(11)} . \color{green}{(p)} + \color{orange}{(11)} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ap-6a+11p-11.6& \text{Uitwerken } \\ & =ap-6a+11p-66 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-19}{16})(\frac{5}{15}+b)& =(\color{red}{a}+\color{orange}{\frac{19}{16}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{19}{16})} . \color{green}{(b)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}a+\frac{19}{16}b+\frac{19}{16}.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}a+\frac{19}{16}b+\frac{19}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-13}{4}-p)(\frac{-13}{20}-a)& =(\color{red}{-p}+\color{orange}{\frac{-13}{4}}).(\color{green}{-a}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{20}p+\frac{13}{4}a+\frac{13}{4}.\frac{13}{20}& \text{Uitwerken } \\ & =ap+\frac{13}{20}p+\frac{13}{4}a+\frac{169}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{5}+q)(p-\frac{-5}{8})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{8}q+4p+4.\frac{5}{8}& \text{Uitwerken } \\ & =pq+\frac{5}{8}q+4p+\frac{20}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{8}q+4p+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-3}{17})(8-b)& =(\color{red}{a}+\color{orange}{\frac{-3}{17}}).(\color{green}{-b}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{-3}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -ab+8a+\frac{3}{17}b-\frac{3}{17}.8& \text{Uitwerken } \\ & =-ab+8a+\frac{3}{17}b-\frac{24}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{11}-x)(q+\frac{-15}{18})& =(\color{red}{-x}+\color{orange}{\frac{5}{11}}).(\color{green}{q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{5}{11})} . \color{green}{(q)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{6}x+\frac{5}{11}q-\frac{5}{11}.\frac{5}{6}& \text{Uitwerken } \\ & =-qx+\frac{5}{6}x+\frac{5}{11}q-\frac{25}{66} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{10}{4})(\frac{-6}{14}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{7}x-\frac{5}{2}a+\frac{5}{2}.\frac{3}{7}& \text{Uitwerken } \\ & =ax-\frac{3}{7}x-\frac{5}{2}a+\frac{15}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}((-4)-x)(\frac{-7}{7}+b)& =(\color{red}{-x}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x-4b+4.1& \text{Uitwerken } \\ & =-bx+1x-4b+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-14}{11})(q+\frac{-13}{2})& =(\color{red}{x}+\color{orange}{\frac{14}{11}}).(\color{green}{q}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{2}x+\frac{14}{11}q-\frac{14}{11}.\frac{13}{2}& \text{Uitwerken } \\ & =qx-\frac{13}{2}x+\frac{14}{11}q-\frac{182}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{13}{2}x+\frac{14}{11}q-\frac{91}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{7}+b)(p+\frac{1}{17})& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{17}b+\frac{3}{7}p+\frac{3}{7}.\frac{1}{17}& \text{Uitwerken } \\ & =bp+\frac{1}{17}b+\frac{3}{7}p+\frac{3}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{4}-b)(x-\frac{-4}{7})& =(\color{red}{-b}+\color{orange}{\frac{11}{4}}).(\color{green}{x}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{11}{4})} . \color{green}{(x)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{7}b+\frac{11}{4}x+\frac{11}{4}.\frac{4}{7}& \text{Uitwerken } \\ & =-bx-\frac{4}{7}b+\frac{11}{4}x+\frac{44}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{4}{7}b+\frac{11}{4}x+\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{19}+p)(q-\frac{-12}{6})& =(\color{red}{p}+\color{orange}{\frac{-17}{19}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p-\frac{17}{19}q-\frac{17}{19}.2& \text{Uitwerken } \\ & =pq+2p-\frac{17}{19}q-\frac{34}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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