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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{6}{10}-b)(p-\frac{2}{19})& =(\color{red}{-b}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{19}b+\frac{3}{5}p-\frac{3}{5}.\frac{2}{19}& \text{Uitwerken } \\ & =-bp+\frac{2}{19}b+\frac{3}{5}p-\frac{6}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{19}+p)(b-\frac{-3}{3})& =(\color{red}{p}+\color{orange}{\frac{-18}{19}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-18}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-\frac{18}{19}b-\frac{18}{19}.1& \text{Uitwerken } \\ & =bp+1p-\frac{18}{19}b-\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{5}{11})(\frac{-20}{11}-a)& =(\color{red}{p}+\color{orange}{\frac{-5}{11}}).(\color{green}{-a}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{20}{11}p+\frac{5}{11}a+\frac{5}{11}.\frac{20}{11}& \text{Uitwerken } \\ & =-ap-\frac{20}{11}p+\frac{5}{11}a+\frac{100}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{14}{13})(\frac{14}{5}+x)& =(\color{red}{q}+\color{orange}{\frac{-14}{13}}).(\color{green}{x}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{14}{5}q-\frac{14}{13}x-\frac{14}{13}.\frac{14}{5}& \text{Uitwerken } \\ & =qx+\frac{14}{5}q-\frac{14}{13}x-\frac{196}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-13}{18}+p)(\frac{6}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-13}{18}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}p-\frac{13}{18}b-\frac{13}{18}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}p-\frac{13}{18}b-\frac{13}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{-7}{20})(\frac{13}{6}-q)& =(\color{red}{a}+\color{orange}{\frac{7}{20}}).(\color{green}{-q}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{7}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{13}{6}a-\frac{7}{20}q+\frac{7}{20}.\frac{13}{6}& \text{Uitwerken } \\ & =-aq+\frac{13}{6}a-\frac{7}{20}q+\frac{91}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{17}{17}+x)(x+\frac{6}{9})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{3}x+1x+1.\frac{2}{3}& \text{Uitwerken } \\ & =x^2+(\frac{2}{3}+1)x+\frac{2}{3} & \text{Neem samen} \\ &=x^2+\frac{5}{3}x+\frac{2}{3} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-17}{4}-a)(\frac{-3}{16}+p)& =(\color{red}{-a}+\color{orange}{\frac{-17}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{16}a-\frac{17}{4}p+\frac{17}{4}.\frac{3}{16}& \text{Uitwerken } \\ & =-ap+\frac{3}{16}a-\frac{17}{4}p+\frac{51}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-20}{10}-q)(\frac{16}{8}+q)& =(\color{red}{-q}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qq-2q-2q-2.2& \text{Uitwerken } \\ & =-q^2+((-2)+(-2))q-4 & \text{Neem samen} \\ &=-q^2-4q-4 & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(x-\frac{19}{10})(16-p)& =(\color{red}{x}+\color{orange}{\frac{-19}{10}}).(\color{green}{-p}+\color{blue}{16})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(16)} + \color{orange}{(\frac{-19}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = -px+16x+\frac{19}{10}p-\frac{19}{10}.16& \text{Uitwerken } \\ & =-px+16x+\frac{19}{10}p-\frac{304}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+16x+\frac{19}{10}p-\frac{152}{5} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{-7}{3})(\frac{2}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{-p}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{2}{11}p+\frac{7}{3}p-\frac{7}{3}.\frac{2}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{2}{11}+\frac{7}{3})p-\frac{14}{33} & \text{Neem samen} \\ &=-p^2+\frac{83}{33}p-\frac{14}{33} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{20}-q)(x+\frac{20}{10})& =(\color{red}{-q}+\color{orange}{\frac{-3}{4}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2q-\frac{3}{4}x-\frac{3}{4}.2& \text{Uitwerken } \\ & =-qx-2q-\frac{3}{4}x-\frac{6}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-2q-\frac{3}{4}x-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)