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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-16}{5}+a)(x-\frac{2}{2})& =(\color{red}{a}+\color{orange}{\frac{-16}{5}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-16}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a-\frac{16}{5}x+\frac{16}{5}.1& \text{Uitwerken } \\ & =ax-1a-\frac{16}{5}x+\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-10}{20})(p+\frac{-20}{16})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{4}p+\frac{1}{2}p-\frac{1}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{4})+\frac{1}{2})p-(\frac{-5}{8}) & \text{Neem samen} \\ &=p^2-\frac{3}{4}p-(\frac{-5}{8}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-15}{8}-a)(\frac{9}{19}-a)& =(\color{red}{-a}+\color{orange}{\frac{-15}{8}}).(\color{green}{-a}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{19}a+\frac{15}{8}a-\frac{15}{8}.\frac{9}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{19})+\frac{15}{8})a-(\frac{-135}{152}) & \text{Neem samen} \\ &=a^2+\frac{213}{152}a-(\frac{-135}{152}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(x+\frac{-17}{6})(\frac{6}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{-17}{6}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qx+2x-\frac{17}{6}q-\frac{17}{6}.2& \text{Uitwerken } \\ & =qx+2x-\frac{17}{6}q-\frac{34}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+2x-\frac{17}{6}q-\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(q-(-20))(x-\frac{-12}{12})& =(\color{red}{q}+\color{orange}{20}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(20)} . \color{green}{(x)} + \color{orange}{(20)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1q+20x+20.1& \text{Uitwerken } \\ & =qx+1q+20x+20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{5}{5}+x)(\frac{-13}{10}-x)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{13}{10}x-1x-1.\frac{13}{10}& \text{Uitwerken } \\ & =-x^2+((\frac{-13}{10})+(-1))x-\frac{13}{10} & \text{Neem samen} \\ &=-x^2-\frac{23}{10}x-\frac{13}{10} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{4}{2}+p)(\frac{-3}{9}+a)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{3}p+2a-2.\frac{1}{3}& \text{Uitwerken } \\ & =ap-\frac{1}{3}p+2a-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{10}{7})(p+\frac{11}{14})& =(\color{red}{b}+\color{orange}{\frac{10}{7}}).(\color{green}{p}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{14}b+\frac{10}{7}p+\frac{10}{7}.\frac{11}{14}& \text{Uitwerken } \\ & =bp+\frac{11}{14}b+\frac{10}{7}p+\frac{110}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{11}{14}b+\frac{10}{7}p+\frac{55}{49} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{13}{3}-p)(x+\frac{-1}{19})& =(\color{red}{-p}+\color{orange}{\frac{13}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{13}{3})} . \color{green}{(x)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{19}p+\frac{13}{3}x-\frac{13}{3}.\frac{1}{19}& \text{Uitwerken } \\ & =-px+\frac{1}{19}p+\frac{13}{3}x-\frac{13}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-8}{14}-p)(p-\frac{15}{9})& =(\color{red}{-p}+\color{orange}{\frac{-4}{7}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{5}{3}p-\frac{4}{7}p+\frac{4}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{5}{3}+(\frac{-4}{7}))p+(\frac{-20}{21}) & \text{Neem samen} \\ &=-p^2+\frac{23}{21}p+(\frac{-20}{21}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-9}{9}+b)(\frac{-16}{7}-b)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{16}{7}b+1b+1.\frac{16}{7}& \text{Uitwerken } \\ & =-b^2+((\frac{-16}{7})+1)b+(\frac{-16}{7}) & \text{Neem samen} \\ &=-b^2-\frac{9}{7}b+(\frac{-16}{7}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{13}{5}+x)(\frac{-2}{14}-q)& =(\color{red}{x}+\color{orange}{\frac{13}{5}}).(\color{green}{-q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{13}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{7}x-\frac{13}{5}q-\frac{13}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =-qx-\frac{1}{7}x-\frac{13}{5}q-\frac{13}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)