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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-16}{8})(x+\frac{7}{14})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}q+2x+2.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}q+2x+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{2}q+2x+1 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{7}{9}+p)(\frac{-13}{15}+p)& =(\color{red}{p}+\color{orange}{\frac{7}{9}}).(\color{green}{p}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{15}p+\frac{7}{9}p-\frac{7}{9}.\frac{13}{15}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{15})+\frac{7}{9})p-(\frac{-91}{135}) & \text{Neem samen} \\ &=p^2-\frac{4}{45}p-(\frac{-91}{135}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{14}{12}+q)(13+q)& =(\color{red}{q}+\color{orange}{\frac{7}{6}}).(\color{green}{q}+\color{blue}{13})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(13)} + \color{orange}{(\frac{7}{6})} . \color{green}{(q)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = qq+13q+\frac{7}{6}q+\frac{7}{6}.13& \text{Uitwerken } \\ & =q^2+(13+\frac{7}{6})q+\frac{91}{6} & \text{Neem samen} \\ &=q^2+\frac{85}{6}q+\frac{91}{6} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{7}{12}+x)(\frac{8}{16}+q)& =(\color{red}{x}+\color{orange}{\frac{7}{12}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{12})} . \color{green}{(q)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}x+\frac{7}{12}q+\frac{7}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}x+\frac{7}{12}q+\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-2}{8}+q)(x-\frac{13}{8})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{8}q-\frac{1}{4}x+\frac{1}{4}.\frac{13}{8}& \text{Uitwerken } \\ & =qx-\frac{13}{8}q-\frac{1}{4}x+\frac{13}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-17}{16}+a)(a+(-7))& =(\color{red}{a}+\color{orange}{\frac{-17}{16}}).(\color{green}{a}+\color{blue}{(-7)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-7)} + \color{orange}{(\frac{-17}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = aa-7a-\frac{17}{16}a+\frac{17}{16}.7& \text{Uitwerken } \\ & =a^2+((-7)+(\frac{-17}{16}))a+\frac{119}{16} & \text{Neem samen} \\ &=a^2-\frac{129}{16}a+\frac{119}{16} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(11-q)(\frac{14}{15}+q)& =(\color{red}{-q}+\color{orange}{11}).(\color{green}{q}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(11)} . \color{green}{(q)} + \color{orange}{(11)} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{14}{15}q+11q+11.\frac{14}{15}& \text{Uitwerken } \\ & =-q^2+((\frac{-14}{15})+11)q+(\frac{-154}{15}) & \text{Neem samen} \\ &=-q^2+\frac{151}{15}q+(\frac{-154}{15}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(b+\frac{-12}{8})(\frac{16}{3}+q)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{3}b-\frac{3}{2}q-\frac{3}{2}.\frac{16}{3}& \text{Uitwerken } \\ & =bq+\frac{16}{3}b-\frac{3}{2}q-\frac{48}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{16}{3}b-\frac{3}{2}q-8 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p-(-9))(p-\frac{-13}{7})& =(\color{red}{p}+\color{orange}{9}).(\color{green}{p}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(9)} . \color{green}{(p)} + \color{orange}{(9)} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{7}p+9p+9.\frac{13}{7}& \text{Uitwerken } \\ & =p^2+(\frac{13}{7}+9)p+\frac{117}{7} & \text{Neem samen} \\ &=p^2+\frac{76}{7}p+\frac{117}{7} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{19}-x)(\frac{-5}{2}-q)& =(\color{red}{-x}+\color{orange}{\frac{-3}{19}}).(\color{green}{-q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{2}x+\frac{3}{19}q+\frac{3}{19}.\frac{5}{2}& \text{Uitwerken } \\ & =qx+\frac{5}{2}x+\frac{3}{19}q+\frac{15}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{11}{7}-b)(q+\frac{11}{19})& =(\color{red}{-b}+\color{orange}{\frac{11}{7}}).(\color{green}{q}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{11}{7})} . \color{green}{(q)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{19}b+\frac{11}{7}q+\frac{11}{7}.\frac{11}{19}& \text{Uitwerken } \\ & =-bq-\frac{11}{19}b+\frac{11}{7}q+\frac{121}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-10}{12}-q)(\frac{-6}{14}-x)& =(\color{red}{-q}+\color{orange}{\frac{-5}{6}}).(\color{green}{-x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{7}q+\frac{5}{6}x+\frac{5}{6}.\frac{3}{7}& \text{Uitwerken } \\ & =qx+\frac{3}{7}q+\frac{5}{6}x+\frac{15}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{7}q+\frac{5}{6}x+\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)