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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-11}{20})(\frac{8}{3}-a)& =(\color{red}{a}+\color{orange}{\frac{-11}{20}}).(\color{green}{-a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{8}{3}a+\frac{11}{20}a-\frac{11}{20}.\frac{8}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{8}{3}+\frac{11}{20})a-\frac{88}{60} & \text{Neem samen} \\ &=-a^2+\frac{193}{60}a-\frac{88}{60} & \text{Maak de som} \\ &=-a^2+\frac{193}{60}a-\frac{22}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{7}+p)(\frac{-2}{3}+x)& =(\color{red}{p}+\color{orange}{\frac{-9}{7}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{3}p-\frac{9}{7}x+\frac{9}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =px-\frac{2}{3}p-\frac{9}{7}x+\frac{18}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{3}p-\frac{9}{7}x+\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{8}{5}-b)(\frac{-15}{20}+q)& =(\color{red}{-b}+\color{orange}{\frac{8}{5}}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{4}b+\frac{8}{5}q-\frac{8}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =-bq+\frac{3}{4}b+\frac{8}{5}q-\frac{24}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{3}{4}b+\frac{8}{5}q-\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-10}{8}-a)(q+\frac{-6}{11})& =(\color{red}{-a}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{6}{11}a-\frac{5}{4}q+\frac{5}{4}.\frac{6}{11}& \text{Uitwerken } \\ & =-aq+\frac{6}{11}a-\frac{5}{4}q+\frac{30}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{6}{11}a-\frac{5}{4}q+\frac{15}{22} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-14}{17}-a)(b+\frac{-11}{15})& =(\color{red}{-a}+\color{orange}{\frac{-14}{17}}).(\color{green}{b}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{15}a-\frac{14}{17}b+\frac{14}{17}.\frac{11}{15}& \text{Uitwerken } \\ & =-ab+\frac{11}{15}a-\frac{14}{17}b+\frac{154}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{10}{7})(\frac{14}{8}-a)& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{-a}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{4}x-\frac{10}{7}a+\frac{10}{7}.\frac{7}{4}& \text{Uitwerken } \\ & =-ax+\frac{7}{4}x-\frac{10}{7}a+\frac{70}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{7}{4}x-\frac{10}{7}a+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q-\frac{-13}{7})(\frac{3}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{13}{7}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{13}{7})} . \color{green}{(x)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}q+\frac{13}{7}x+\frac{13}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}q+\frac{13}{7}x+\frac{39}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-1}{18}+b)(\frac{-19}{18}+x)& =(\color{red}{b}+\color{orange}{\frac{-1}{18}}).(\color{green}{x}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{18}b-\frac{1}{18}x+\frac{1}{18}.\frac{19}{18}& \text{Uitwerken } \\ & =bx-\frac{19}{18}b-\frac{1}{18}x+\frac{19}{324} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{-1}{13})(\frac{1}{13}-q)& =(\color{red}{p}+\color{orange}{\frac{1}{13}}).(\color{green}{-q}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{1}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{13}p-\frac{1}{13}q+\frac{1}{13}.\frac{1}{13}& \text{Uitwerken } \\ & =-pq+\frac{1}{13}p-\frac{1}{13}q+\frac{1}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}((-18)-b)(\frac{-16}{11}-b)& =(\color{red}{-b}+\color{orange}{(-18)}).(\color{green}{-b}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(-18)} . \color{green}{(-b)} + \color{orange}{(-18)} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{11}b+18b+18.\frac{16}{11}& \text{Uitwerken } \\ & =b^2+(\frac{16}{11}+18)b+\frac{288}{11} & \text{Neem samen} \\ &=b^2+\frac{214}{11}b+\frac{288}{11} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(a-\frac{-6}{5})(b+\frac{3}{6})& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a+\frac{6}{5}b+\frac{6}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a+\frac{6}{5}b+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{2}a+\frac{6}{5}b+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a-\frac{-18}{5})(a+3)& =(\color{red}{a}+\color{orange}{\frac{18}{5}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{18}{5})} . \color{green}{(a)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aa+3a+\frac{18}{5}a+\frac{18}{5}.3& \text{Uitwerken } \\ & =a^2+(3+\frac{18}{5})a+\frac{54}{5} & \text{Neem samen} \\ &=a^2+\frac{33}{5}a+\frac{54}{5} & \text{Maak de som} \\\end{align}\)