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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{18}{7}+b)(p-\frac{2}{17})& =(\color{red}{b}+\color{orange}{\frac{18}{7}}).(\color{green}{p}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{18}{7})} . \color{green}{(p)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{17}b+\frac{18}{7}p-\frac{18}{7}.\frac{2}{17}& \text{Uitwerken } \\ & =bp-\frac{2}{17}b+\frac{18}{7}p-\frac{36}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-13}{7}+a)(p-\frac{-20}{4})& =(\color{red}{a}+\color{orange}{\frac{-13}{7}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(5)} + \color{orange}{(\frac{-13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ap+5a-\frac{13}{7}p-\frac{13}{7}.5& \text{Uitwerken } \\ & =ap+5a-\frac{13}{7}p-\frac{65}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-3}{7}+q)(b-\frac{-13}{10})& =(\color{red}{q}+\color{orange}{\frac{-3}{7}}).(\color{green}{b}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{10}q-\frac{3}{7}b-\frac{3}{7}.\frac{13}{10}& \text{Uitwerken } \\ & =bq+\frac{13}{10}q-\frac{3}{7}b-\frac{39}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{-20}{10})(a-\frac{-16}{17})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{16}{17}a+2a+2.\frac{16}{17}& \text{Uitwerken } \\ & =a^2+(\frac{16}{17}+2)a+\frac{32}{17} & \text{Neem samen} \\ &=a^2+\frac{50}{17}a+\frac{32}{17} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(x-\frac{1}{13})(\frac{13}{18}-p)& =(\color{red}{x}+\color{orange}{\frac{-1}{13}}).(\color{green}{-p}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{18}x+\frac{1}{13}p-\frac{1}{13}.\frac{13}{18}& \text{Uitwerken } \\ & =-px+\frac{13}{18}x+\frac{1}{13}p-\frac{13}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{13}{18}x+\frac{1}{13}p-\frac{1}{18} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{7}{9}+q)(1-b)& =(\color{red}{q}+\color{orange}{\frac{7}{9}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq+1q-\frac{7}{9}b+\frac{7}{9}.1& \text{Uitwerken } \\ & =-bq+1q-\frac{7}{9}b+\frac{7}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{6}+q)(b-\frac{-1}{11})& =(\color{red}{q}+\color{orange}{\frac{-17}{6}}).(\color{green}{b}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{11}q-\frac{17}{6}b-\frac{17}{6}.\frac{1}{11}& \text{Uitwerken } \\ & =bq+\frac{1}{11}q-\frac{17}{6}b-\frac{17}{66} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{3}{13}+q)(b-\frac{-15}{5})& =(\color{red}{q}+\color{orange}{\frac{3}{13}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{3}{13})} . \color{green}{(b)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3q+\frac{3}{13}b+\frac{3}{13}.3& \text{Uitwerken } \\ & =bq+3q+\frac{3}{13}b+\frac{9}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-16}{16}-p)(a-\frac{7}{7})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1p-1a+1.1& \text{Uitwerken } \\ & =-ap+1p-1a+1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{-18}{4})(\frac{18}{4}-x)& =(\color{red}{x}+\color{orange}{\frac{-9}{2}}).(\color{green}{-x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{9}{2}x+\frac{9}{2}x-\frac{9}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =-x^2+(\frac{9}{2}+\frac{9}{2})x-\frac{81}{4} & \text{Neem samen} \\ &=-x^2+\frac{18}{2}x-\frac{81}{4} & \text{Maak de som} \\ &=-x^2+9x-\frac{81}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(q+\frac{17}{20})(p+10)& =(\color{red}{q}+\color{orange}{\frac{17}{20}}).(\color{green}{p}+\color{blue}{10})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(10)} + \color{orange}{(\frac{17}{20})} . \color{green}{(p)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = pq+10q+\frac{17}{20}p+\frac{17}{20}.10& \text{Uitwerken } \\ & =pq+10q+\frac{17}{20}p+\frac{170}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+10q+\frac{17}{20}p+\frac{17}{2} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{16}{19}-b)(\frac{12}{16}+b)& =(\color{red}{-b}+\color{orange}{\frac{16}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{4}b+\frac{16}{19}b+\frac{16}{19}.\frac{3}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{4})+\frac{16}{19})b+(\frac{-48}{76}) & \text{Neem samen} \\ &=-b^2+\frac{7}{76}b+(\frac{-48}{76}) & \text{Maak de som} \\ &=-b^2+\frac{7}{76}b+(\frac{-12}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)