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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{17}-q)(p-(-12))& =(\color{red}{-q}+\color{orange}{\frac{-15}{17}}).(\color{green}{p}+\color{blue}{12})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(12)} + \color{orange}{(\frac{-15}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -pq-12q-\frac{15}{17}p-\frac{15}{17}.12& \text{Uitwerken } \\ & =-pq-12q-\frac{15}{17}p-\frac{180}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-10}{15}-p)(\frac{-9}{3}+q)& =(\color{red}{-p}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -pq+3p-\frac{2}{3}q+\frac{2}{3}.3& \text{Uitwerken } \\ & =-pq+3p-\frac{2}{3}q+\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+3p-\frac{2}{3}q+2 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q+\frac{-3}{5})(p-\frac{-18}{3})& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{-3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = pq+6q-\frac{3}{5}p-\frac{3}{5}.6& \text{Uitwerken } \\ & =pq+6q-\frac{3}{5}p-\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-20}{20}-x)(\frac{-4}{19}+a)& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{19}x-1a+1.\frac{4}{19}& \text{Uitwerken } \\ & =-ax+\frac{4}{19}x-1a+\frac{4}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-10}{7}+b)(q-\frac{-11}{2})& =(\color{red}{b}+\color{orange}{\frac{-10}{7}}).(\color{green}{q}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{2}b-\frac{10}{7}q-\frac{10}{7}.\frac{11}{2}& \text{Uitwerken } \\ & =bq+\frac{11}{2}b-\frac{10}{7}q-\frac{110}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{11}{2}b-\frac{10}{7}q-\frac{55}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{1}{4}-q)(b+\frac{-18}{9})& =(\color{red}{-q}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bq+2q+\frac{1}{4}b-\frac{1}{4}.2& \text{Uitwerken } \\ & =-bq+2q+\frac{1}{4}b-\frac{2}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+2q+\frac{1}{4}b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b+\frac{6}{14})(q-\frac{7}{13})& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{q}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{13}b+\frac{3}{7}q-\frac{3}{7}.\frac{7}{13}& \text{Uitwerken } \\ & =bq-\frac{7}{13}b+\frac{3}{7}q-\frac{21}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{7}{13}b+\frac{3}{7}q-\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x+\frac{18}{8})(x-\frac{-2}{10})& =(\color{red}{x}+\color{orange}{\frac{9}{4}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{9}{4})} . \color{green}{(x)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{5}x+\frac{9}{4}x+\frac{9}{4}.\frac{1}{5}& \text{Uitwerken } \\ & =x^2+(\frac{1}{5}+\frac{9}{4})x+\frac{9}{20} & \text{Neem samen} \\ &=x^2+\frac{49}{20}x+\frac{9}{20} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{-18}{12}-a)(a+13)& =(\color{red}{-a}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{13})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(13)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = -aa-13a-\frac{3}{2}a-\frac{3}{2}.13& \text{Uitwerken } \\ & =-a^2+((-13)+(\frac{-3}{2}))a-\frac{39}{2} & \text{Neem samen} \\ &=-a^2-\frac{29}{2}a-\frac{39}{2} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(q-\frac{15}{16})(b-\frac{6}{19})& =(\color{red}{q}+\color{orange}{\frac{-15}{16}}).(\color{green}{b}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{6}{19}q-\frac{15}{16}b+\frac{15}{16}.\frac{6}{19}& \text{Uitwerken } \\ & =bq-\frac{6}{19}q-\frac{15}{16}b+\frac{90}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{6}{19}q-\frac{15}{16}b+\frac{45}{152} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-\frac{-6}{15})(\frac{11}{4}-x)& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{-x}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{11}{4}b-\frac{2}{5}x+\frac{2}{5}.\frac{11}{4}& \text{Uitwerken } \\ & =-bx+\frac{11}{4}b-\frac{2}{5}x+\frac{22}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{11}{4}b-\frac{2}{5}x+\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q-\frac{-12}{6})(\frac{-13}{19}+p)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{19}q+2p-2.\frac{13}{19}& \text{Uitwerken } \\ & =pq-\frac{13}{19}q+2p-\frac{26}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)