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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{12}{20}-b)(\frac{15}{5}+p)& =(\color{red}{-b}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(3)} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bp-3b+\frac{3}{5}p+\frac{3}{5}.3& \text{Uitwerken } \\ & =-bp-3b+\frac{3}{5}p+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{-17}{4})(\frac{12}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{17}{4}}).(\color{green}{a}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(\frac{17}{4})} . \color{green}{(a)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ax+6x+\frac{17}{4}a+\frac{17}{4}.6& \text{Uitwerken } \\ & =ax+6x+\frac{17}{4}a+\frac{102}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+6x+\frac{17}{4}a+\frac{51}{2} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{16}{11}+b)(q-\frac{14}{9})& =(\color{red}{b}+\color{orange}{\frac{16}{11}}).(\color{green}{q}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{9}b+\frac{16}{11}q-\frac{16}{11}.\frac{14}{9}& \text{Uitwerken } \\ & =bq-\frac{14}{9}b+\frac{16}{11}q-\frac{224}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{20}{2}+q)(16-b)& =(\color{red}{q}+\color{orange}{10}).(\color{green}{-b}+\color{blue}{16})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(16)} + \color{orange}{(10)} . \color{green}{(-b)} + \color{orange}{(10)} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = -bq+16q-10b+10.16& \text{Uitwerken } \\ & =-bq+16q-10b+160 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{16}{5})(\frac{14}{6}+q)& =(\color{red}{a}+\color{orange}{\frac{-16}{5}}).(\color{green}{q}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{3}a-\frac{16}{5}q-\frac{16}{5}.\frac{7}{3}& \text{Uitwerken } \\ & =aq+\frac{7}{3}a-\frac{16}{5}q-\frac{112}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{10}{10})(a-\frac{20}{7})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{20}{7}p+1a-1.\frac{20}{7}& \text{Uitwerken } \\ & =ap-\frac{20}{7}p+1a-\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{9}{18})(\frac{-9}{14}-x)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{14}a-\frac{1}{2}x-\frac{1}{2}.\frac{9}{14}& \text{Uitwerken } \\ & =-ax-\frac{9}{14}a-\frac{1}{2}x-\frac{9}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{10}{17})(p-\frac{-5}{5})& =(\color{red}{b}+\color{orange}{\frac{-10}{17}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1b-\frac{10}{17}p-\frac{10}{17}.1& \text{Uitwerken } \\ & =bp+1b-\frac{10}{17}p-\frac{10}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{4}{11}-b)(\frac{-11}{14}-p)& =(\color{red}{-b}+\color{orange}{\frac{4}{11}}).(\color{green}{-p}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{4}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{14}b-\frac{4}{11}p-\frac{4}{11}.\frac{11}{14}& \text{Uitwerken } \\ & =bp+\frac{11}{14}b-\frac{4}{11}p-\frac{44}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{11}{14}b-\frac{4}{11}p-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q-\frac{-13}{18})(b+\frac{17}{4})& =(\color{red}{q}+\color{orange}{\frac{13}{18}}).(\color{green}{b}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{4}q+\frac{13}{18}b+\frac{13}{18}.\frac{17}{4}& \text{Uitwerken } \\ & =bq+\frac{17}{4}q+\frac{13}{18}b+\frac{221}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q+\frac{-9}{7})(q-\frac{-4}{14})& =(\color{red}{q}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{7}q-\frac{9}{7}q-\frac{9}{7}.\frac{2}{7}& \text{Uitwerken } \\ & =q^2+(\frac{2}{7}+(\frac{-9}{7}))q-(\frac{-18}{49}) & \text{Neem samen} \\ &=q^2-\frac{7}{7}q-(\frac{-18}{49}) & \text{Maak de som} \\ &=q^2-1q+\frac{18}{49} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
12. \(\begin{align}(x-\frac{-4}{12})(\frac{19}{5}-a)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{-a}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{5}x-\frac{1}{3}a+\frac{1}{3}.\frac{19}{5}& \text{Uitwerken } \\ & =-ax+\frac{19}{5}x-\frac{1}{3}a+\frac{19}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)