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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-16}{10}+x)(16+x)& =(\color{red}{x}+\color{orange}{\frac{-8}{5}}).(\color{green}{x}+\color{blue}{16})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(16)} + \color{orange}{(\frac{-8}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = xx+16x-\frac{8}{5}x-\frac{8}{5}.16& \text{Uitwerken } \\ & =x^2+(16+(\frac{-8}{5}))x-(\frac{-128}{5}) & \text{Neem samen} \\ &=x^2+\frac{72}{5}x-(\frac{-128}{5}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(b-\frac{-2}{10})(\frac{19}{7}+p)& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{7}b+\frac{1}{5}p+\frac{1}{5}.\frac{19}{7}& \text{Uitwerken } \\ & =bp+\frac{19}{7}b+\frac{1}{5}p+\frac{19}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{-6}{3})(\frac{4}{9}-q)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{9}b+2q-2.\frac{4}{9}& \text{Uitwerken } \\ & =-bq+\frac{4}{9}b+2q-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{17}{3}-q)(\frac{-20}{2}+b)& =(\color{red}{-q}+\color{orange}{\frac{17}{3}}).(\color{green}{b}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-10)} + \color{orange}{(\frac{17}{3})} . \color{green}{(b)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -bq+10q+\frac{17}{3}b-\frac{17}{3}.10& \text{Uitwerken } \\ & =-bq+10q+\frac{17}{3}b-\frac{170}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{4}{6}+x)(\frac{20}{15}-p)& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{-p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{4}{3}x-\frac{2}{3}p+\frac{2}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =-px+\frac{4}{3}x-\frac{2}{3}p+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{11}{13})(\frac{17}{6}-p)& =(\color{red}{b}+\color{orange}{\frac{-11}{13}}).(\color{green}{-p}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{6}b+\frac{11}{13}p-\frac{11}{13}.\frac{17}{6}& \text{Uitwerken } \\ & =-bp+\frac{17}{6}b+\frac{11}{13}p-\frac{187}{78} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-3}{3}-q)(\frac{14}{20}-a)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{10}q+1a-1.\frac{7}{10}& \text{Uitwerken } \\ & =aq-\frac{7}{10}q+1a-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-(-3))(a-\frac{-3}{14})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{14}b+3a+3.\frac{3}{14}& \text{Uitwerken } \\ & =ab+\frac{3}{14}b+3a+\frac{9}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-15}{10}-q)(\frac{-15}{20}+a)& =(\color{red}{-q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{4}q-\frac{3}{2}a+\frac{3}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =-aq+\frac{3}{4}q-\frac{3}{2}a+\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{2}{6}+x)(\frac{13}{7}+q)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{7}x+\frac{1}{3}q+\frac{1}{3}.\frac{13}{7}& \text{Uitwerken } \\ & =qx+\frac{13}{7}x+\frac{1}{3}q+\frac{13}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-20}{5}-x)(q-\frac{1}{19})& =(\color{red}{-x}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{19}x-4q+4.\frac{1}{19}& \text{Uitwerken } \\ & =-qx+\frac{1}{19}x-4q+\frac{4}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{-12}{10})(\frac{-20}{8}-a)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{2}a-\frac{6}{5}a-\frac{6}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{2})+(\frac{-6}{5}))a-\frac{30}{10} & \text{Neem samen} \\ &=-a^2-\frac{37}{10}a-\frac{30}{10} & \text{Maak de som} \\ &=-a^2-\frac{37}{10}a-3 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)