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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{19}{17}+p)(7-a)& =(\color{red}{p}+\color{orange}{\frac{19}{17}}).(\color{green}{-a}+\color{blue}{7})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(7)} + \color{orange}{(\frac{19}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -ap+7p-\frac{19}{17}a+\frac{19}{17}.7& \text{Uitwerken } \\ & =-ap+7p-\frac{19}{17}a+\frac{133}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{18}{11})(\frac{3}{14}-p)& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{-p}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{18}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{14}x-\frac{18}{11}p+\frac{18}{11}.\frac{3}{14}& \text{Uitwerken } \\ & =-px+\frac{3}{14}x-\frac{18}{11}p+\frac{54}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{3}{14}x-\frac{18}{11}p+\frac{27}{77} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q-\frac{-20}{18})(\frac{15}{5}+q)& =(\color{red}{q}+\color{orange}{\frac{10}{9}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{10}{9})} . \color{green}{(q)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qq+3q+\frac{10}{9}q+\frac{10}{9}.3& \text{Uitwerken } \\ & =q^2+(3+\frac{10}{9})q+\frac{30}{9} & \text{Neem samen} \\ &=q^2+\frac{37}{9}q+\frac{30}{9} & \text{Maak de som} \\ &=q^2+\frac{37}{9}q+\frac{10}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(\frac{20}{12}+b)(x+\frac{14}{3})& =(\color{red}{b}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{14}{3}b+\frac{5}{3}x+\frac{5}{3}.\frac{14}{3}& \text{Uitwerken } \\ & =bx+\frac{14}{3}b+\frac{5}{3}x+\frac{70}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{-8}{6})(x-\frac{14}{11})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{11}q+\frac{4}{3}x-\frac{4}{3}.\frac{14}{11}& \text{Uitwerken } \\ & =qx-\frac{14}{11}q+\frac{4}{3}x-\frac{56}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-17}{5}+q)(b+\frac{-13}{16})& =(\color{red}{q}+\color{orange}{\frac{-17}{5}}).(\color{green}{b}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{16}q-\frac{17}{5}b+\frac{17}{5}.\frac{13}{16}& \text{Uitwerken } \\ & =bq-\frac{13}{16}q-\frac{17}{5}b+\frac{221}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x-\frac{18}{2})(\frac{17}{10}+a)& =(\color{red}{x}+\color{orange}{(-9)}).(\color{green}{a}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(-9)} . \color{green}{(a)} + \color{orange}{(-9)} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{10}x-9a-9.\frac{17}{10}& \text{Uitwerken } \\ & =ax+\frac{17}{10}x-9a-\frac{153}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(19-b)(\frac{11}{10}+p)& =(\color{red}{-b}+\color{orange}{19}).(\color{green}{p}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(19)} . \color{green}{(p)} + \color{orange}{(19)} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{10}b+19p+19.\frac{11}{10}& \text{Uitwerken } \\ & =-bp-\frac{11}{10}b+19p+\frac{209}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{7}{3}+b)(p+\frac{2}{17})& =(\color{red}{b}+\color{orange}{\frac{7}{3}}).(\color{green}{p}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{17}b+\frac{7}{3}p+\frac{7}{3}.\frac{2}{17}& \text{Uitwerken } \\ & =bp+\frac{2}{17}b+\frac{7}{3}p+\frac{14}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-9}{9})(b-\frac{-12}{4})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bx+3x+1b+1.3& \text{Uitwerken } \\ & =bx+3x+1b+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{2}{7}-a)(\frac{14}{19}+a)& =(\color{red}{-a}+\color{orange}{\frac{2}{7}}).(\color{green}{a}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{14}{19}a+\frac{2}{7}a+\frac{2}{7}.\frac{14}{19}& \text{Uitwerken } \\ & =-a^2+((\frac{-14}{19})+\frac{2}{7})a+(\frac{-28}{133}) & \text{Neem samen} \\ &=-a^2-\frac{60}{133}a+(\frac{-28}{133}) & \text{Maak de som} \\ &=-a^2-\frac{60}{133}a+(\frac{-4}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(p+\frac{11}{20})(a-\frac{-11}{16})& =(\color{red}{p}+\color{orange}{\frac{11}{20}}).(\color{green}{a}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{11}{20})} . \color{green}{(a)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{16}p+\frac{11}{20}a+\frac{11}{20}.\frac{11}{16}& \text{Uitwerken } \\ & =ap+\frac{11}{16}p+\frac{11}{20}a+\frac{121}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)