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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-18}{9})(p-13)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{p}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-13)} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = pq-13q+2p-2.13& \text{Uitwerken } \\ & =pq-13q+2p-26 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-13}{13}+b)(\frac{-7}{12}+b)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{12}b-1b+1.\frac{7}{12}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{12})+(-1))b+\frac{7}{12} & \text{Neem samen} \\ &=b^2-\frac{19}{12}b+\frac{7}{12} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(p+\frac{7}{13})(a+8)& =(\color{red}{p}+\color{orange}{\frac{7}{13}}).(\color{green}{a}+\color{blue}{8})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(8)} + \color{orange}{(\frac{7}{13})} . \color{green}{(a)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ap+8p+\frac{7}{13}a+\frac{7}{13}.8& \text{Uitwerken } \\ & =ap+8p+\frac{7}{13}a+\frac{56}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{5}{19})(\frac{13}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{-5}{19}}).(\color{green}{-b}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{13}{16}q+\frac{5}{19}b-\frac{5}{19}.\frac{13}{16}& \text{Uitwerken } \\ & =-bq+\frac{13}{16}q+\frac{5}{19}b-\frac{65}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-13}{16})(\frac{-13}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{-13}{16}}).(\color{green}{b}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{4}p-\frac{13}{16}b+\frac{13}{16}.\frac{13}{4}& \text{Uitwerken } \\ & =bp-\frac{13}{4}p-\frac{13}{16}b+\frac{169}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-11}{16})(a+\frac{9}{11})& =(\color{red}{x}+\color{orange}{\frac{-11}{16}}).(\color{green}{a}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{11}x-\frac{11}{16}a-\frac{11}{16}.\frac{9}{11}& \text{Uitwerken } \\ & =ax+\frac{9}{11}x-\frac{11}{16}a-\frac{99}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{11}x-\frac{11}{16}a-\frac{9}{16} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{6}{6}-b)(x-\frac{-4}{11})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{11}b+1x+1.\frac{4}{11}& \text{Uitwerken } \\ & =-bx-\frac{4}{11}b+1x+\frac{4}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{14}{4})(\frac{-10}{11}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{p}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{11}a+\frac{7}{2}p-\frac{7}{2}.\frac{10}{11}& \text{Uitwerken } \\ & =ap-\frac{10}{11}a+\frac{7}{2}p-\frac{70}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{11}a+\frac{7}{2}p-\frac{35}{11} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x+\frac{13}{3})(\frac{-9}{15}-x)& =(\color{red}{x}+\color{orange}{\frac{13}{3}}).(\color{green}{-x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{13}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{5}x-\frac{13}{3}x-\frac{13}{3}.\frac{3}{5}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{5})+(\frac{-13}{3}))x-\frac{39}{15} & \text{Neem samen} \\ &=-x^2-\frac{74}{15}x-\frac{39}{15} & \text{Maak de som} \\ &=-x^2-\frac{74}{15}x-\frac{13}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{17}{15}-b)(\frac{-12}{14}+p)& =(\color{red}{-b}+\color{orange}{\frac{17}{15}}).(\color{green}{p}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{17}{15})} . \color{green}{(p)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{6}{7}b+\frac{17}{15}p-\frac{17}{15}.\frac{6}{7}& \text{Uitwerken } \\ & =-bp+\frac{6}{7}b+\frac{17}{15}p-\frac{102}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{6}{7}b+\frac{17}{15}p-\frac{34}{35} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b+\frac{19}{16})(p+\frac{-16}{8})& =(\color{red}{b}+\color{orange}{\frac{19}{16}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{19}{16})} . \color{green}{(p)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bp-2b+\frac{19}{16}p-\frac{19}{16}.2& \text{Uitwerken } \\ & =bp-2b+\frac{19}{16}p-\frac{38}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-2b+\frac{19}{16}p-\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-16}{11}-x)(q-\frac{1}{5})& =(\color{red}{-x}+\color{orange}{\frac{-16}{11}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{5}x-\frac{16}{11}q+\frac{16}{11}.\frac{1}{5}& \text{Uitwerken } \\ & =-qx+\frac{1}{5}x-\frac{16}{11}q+\frac{16}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)