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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{15}+x)(q+\frac{-6}{11})& =(\color{red}{x}+\color{orange}{\frac{-2}{15}}).(\color{green}{q}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{11}x-\frac{2}{15}q+\frac{2}{15}.\frac{6}{11}& \text{Uitwerken } \\ & =qx-\frac{6}{11}x-\frac{2}{15}q+\frac{12}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{6}{11}x-\frac{2}{15}q+\frac{4}{55} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-\frac{15}{8})(b-\frac{10}{11})& =(\color{red}{x}+\color{orange}{\frac{-15}{8}}).(\color{green}{b}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{11}x-\frac{15}{8}b+\frac{15}{8}.\frac{10}{11}& \text{Uitwerken } \\ & =bx-\frac{10}{11}x-\frac{15}{8}b+\frac{150}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{10}{11}x-\frac{15}{8}b+\frac{75}{44} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{16}{9}+p)(\frac{-19}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{16}{9}}).(\color{green}{b}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{16}{9})} . \color{green}{(b)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{9}p+\frac{16}{9}b-\frac{16}{9}.\frac{19}{9}& \text{Uitwerken } \\ & =bp-\frac{19}{9}p+\frac{16}{9}b-\frac{304}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{2}{17})(\frac{-5}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{2}{17}}).(\color{green}{-x}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{2}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{11}a-\frac{2}{17}x-\frac{2}{17}.\frac{5}{11}& \text{Uitwerken } \\ & =-ax-\frac{5}{11}a-\frac{2}{17}x-\frac{10}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-11}{13}-x)(q-\frac{4}{16})& =(\color{red}{-x}+\color{orange}{\frac{-11}{13}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{4}x-\frac{11}{13}q+\frac{11}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =-qx+\frac{1}{4}x-\frac{11}{13}q+\frac{11}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{14}{9})(\frac{-11}{7}+x)& =(\color{red}{a}+\color{orange}{\frac{14}{9}}).(\color{green}{x}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{14}{9})} . \color{green}{(x)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{7}a+\frac{14}{9}x-\frac{14}{9}.\frac{11}{7}& \text{Uitwerken } \\ & =ax-\frac{11}{7}a+\frac{14}{9}x-\frac{154}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{11}{7}a+\frac{14}{9}x-\frac{22}{9} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{19}{4}+q)(\frac{-6}{19}+p)& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{p}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{19}{4})} . \color{green}{(p)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{19}q+\frac{19}{4}p-\frac{19}{4}.\frac{6}{19}& \text{Uitwerken } \\ & =pq-\frac{6}{19}q+\frac{19}{4}p-\frac{114}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{6}{19}q+\frac{19}{4}p-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{9}{11}+p)(b-\frac{-12}{2})& =(\color{red}{p}+\color{orange}{\frac{9}{11}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(6)} + \color{orange}{(\frac{9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bp+6p+\frac{9}{11}b+\frac{9}{11}.6& \text{Uitwerken } \\ & =bp+6p+\frac{9}{11}b+\frac{54}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}((-1)+a)(\frac{-6}{13}-x)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{6}{13}a+1x+1.\frac{6}{13}& \text{Uitwerken } \\ & =-ax-\frac{6}{13}a+1x+\frac{6}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-10}{20}+x)(\frac{20}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{3}x-\frac{1}{2}q-\frac{1}{2}.\frac{20}{3}& \text{Uitwerken } \\ & =qx+\frac{20}{3}x-\frac{1}{2}q-\frac{20}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{20}{3}x-\frac{1}{2}q-\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{-16}{11})(\frac{-2}{3}-a)& =(\color{red}{p}+\color{orange}{\frac{-16}{11}}).(\color{green}{-a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{3}p+\frac{16}{11}a+\frac{16}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =-ap-\frac{2}{3}p+\frac{16}{11}a+\frac{32}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-1}{4}-p)(q+\frac{-10}{14})& =(\color{red}{-p}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{7}p-\frac{1}{4}q+\frac{1}{4}.\frac{5}{7}& \text{Uitwerken } \\ & =-pq+\frac{5}{7}p-\frac{1}{4}q+\frac{5}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)