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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-5}{19})(b+\frac{8}{14})& =(\color{red}{q}+\color{orange}{\frac{5}{19}}).(\color{green}{b}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{5}{19})} . \color{green}{(b)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{7}q+\frac{5}{19}b+\frac{5}{19}.\frac{4}{7}& \text{Uitwerken } \\ & =bq+\frac{4}{7}q+\frac{5}{19}b+\frac{20}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-7}{14})(p-\frac{-18}{13})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{13}b+\frac{1}{2}p+\frac{1}{2}.\frac{18}{13}& \text{Uitwerken } \\ & =bp+\frac{18}{13}b+\frac{1}{2}p+\frac{18}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{18}{13}b+\frac{1}{2}p+\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-19}{10}-q)((-7)+q)& =(\color{red}{-q}+\color{orange}{\frac{-19}{10}}).(\color{green}{q}+\color{blue}{(-7)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-7)} + \color{orange}{(\frac{-19}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -qq+7q-\frac{19}{10}q+\frac{19}{10}.7& \text{Uitwerken } \\ & =-q^2+(7+(\frac{-19}{10}))q+(\frac{-133}{10}) & \text{Neem samen} \\ &=-q^2+\frac{51}{10}q+(\frac{-133}{10}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{13}{2}+b)(p+\frac{1}{18})& =(\color{red}{b}+\color{orange}{\frac{13}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{13}{2})} . \color{green}{(p)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{18}b+\frac{13}{2}p+\frac{13}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =bp+\frac{1}{18}b+\frac{13}{2}p+\frac{13}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-2}{5}+a)(p+\frac{-2}{8})& =(\color{red}{a}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{4}a-\frac{2}{5}p+\frac{2}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =ap-\frac{1}{4}a-\frac{2}{5}p+\frac{2}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{4}a-\frac{2}{5}p+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{15}{7}+x)(\frac{-11}{3}-a)& =(\color{red}{x}+\color{orange}{\frac{15}{7}}).(\color{green}{-a}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{15}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{3}x-\frac{15}{7}a-\frac{15}{7}.\frac{11}{3}& \text{Uitwerken } \\ & =-ax-\frac{11}{3}x-\frac{15}{7}a-\frac{165}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{11}{3}x-\frac{15}{7}a-\frac{55}{7} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{15}{11}-a)(p-\frac{19}{3})& =(\color{red}{-a}+\color{orange}{\frac{15}{11}}).(\color{green}{p}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{3}a+\frac{15}{11}p-\frac{15}{11}.\frac{19}{3}& \text{Uitwerken } \\ & =-ap+\frac{19}{3}a+\frac{15}{11}p-\frac{285}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{19}{3}a+\frac{15}{11}p-\frac{95}{11} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{14}{19}-b)(a-\frac{-20}{12})& =(\color{red}{-b}+\color{orange}{\frac{14}{19}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{3}b+\frac{14}{19}a+\frac{14}{19}.\frac{5}{3}& \text{Uitwerken } \\ & =-ab-\frac{5}{3}b+\frac{14}{19}a+\frac{70}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-11}{17}+x)(16+q)& =(\color{red}{x}+\color{orange}{\frac{-11}{17}}).(\color{green}{q}+\color{blue}{16})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(16)} + \color{orange}{(\frac{-11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = qx+16x-\frac{11}{17}q-\frac{11}{17}.16& \text{Uitwerken } \\ & =qx+16x-\frac{11}{17}q-\frac{176}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{7}{14}+x)(q-\frac{-20}{20})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1x+\frac{1}{2}q+\frac{1}{2}.1& \text{Uitwerken } \\ & =qx+1x+\frac{1}{2}q+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{2}{7}+a)(\frac{-8}{12}-x)& =(\color{red}{a}+\color{orange}{\frac{2}{7}}).(\color{green}{-x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{2}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{2}{3}a-\frac{2}{7}x-\frac{2}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-ax-\frac{2}{3}a-\frac{2}{7}x-\frac{4}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{15}-x)(x+\frac{10}{7})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{10}{7}x-1x-1.\frac{10}{7}& \text{Uitwerken } \\ & =-x^2+((\frac{-10}{7})+(-1))x-\frac{10}{7} & \text{Neem samen} \\ &=-x^2-\frac{17}{7}x-\frac{10}{7} & \text{Maak de som} \\\end{align}\)