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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{2}{8}-x)(b-\frac{-12}{17})& =(\color{red}{-x}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{12}{17}x+\frac{1}{4}b+\frac{1}{4}.\frac{12}{17}& \text{Uitwerken } \\ & =-bx-\frac{12}{17}x+\frac{1}{4}b+\frac{12}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{12}{17}x+\frac{1}{4}b+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-19}{16}-p)(b+\frac{-5}{12})& =(\color{red}{-p}+\color{orange}{\frac{-19}{16}}).(\color{green}{b}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{12}p-\frac{19}{16}b+\frac{19}{16}.\frac{5}{12}& \text{Uitwerken } \\ & =-bp+\frac{5}{12}p-\frac{19}{16}b+\frac{95}{192} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{-1}{11})(\frac{-17}{3}+x)& =(\color{red}{q}+\color{orange}{\frac{-1}{11}}).(\color{green}{x}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{3}q-\frac{1}{11}x+\frac{1}{11}.\frac{17}{3}& \text{Uitwerken } \\ & =qx-\frac{17}{3}q-\frac{1}{11}x+\frac{17}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-7)(\frac{2}{9}-p)& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{-p}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(-7)} . \color{green}{(-p)} + \color{orange}{(-7)} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{9}a+7p-7.\frac{2}{9}& \text{Uitwerken } \\ & =-ap+\frac{2}{9}a+7p-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-7}{10}+x)(a+\frac{-14}{10})& =(\color{red}{x}+\color{orange}{\frac{-7}{10}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{5}x-\frac{7}{10}a+\frac{7}{10}.\frac{7}{5}& \text{Uitwerken } \\ & =ax-\frac{7}{5}x-\frac{7}{10}a+\frac{49}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{3}{17}+a)(p-\frac{11}{3})& =(\color{red}{a}+\color{orange}{\frac{3}{17}}).(\color{green}{p}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{3}{17})} . \color{green}{(p)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{3}a+\frac{3}{17}p-\frac{3}{17}.\frac{11}{3}& \text{Uitwerken } \\ & =ap-\frac{11}{3}a+\frac{3}{17}p-\frac{33}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{11}{3}a+\frac{3}{17}p-\frac{11}{17} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{-7}{12})(\frac{1}{20}+a)& =(\color{red}{b}+\color{orange}{\frac{7}{12}}).(\color{green}{a}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{20}b+\frac{7}{12}a+\frac{7}{12}.\frac{1}{20}& \text{Uitwerken } \\ & =ab+\frac{1}{20}b+\frac{7}{12}a+\frac{7}{240} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{15}{14}-p)(\frac{-13}{15}+q)& =(\color{red}{-p}+\color{orange}{\frac{15}{14}}).(\color{green}{q}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{15}{14})} . \color{green}{(q)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{13}{15}p+\frac{15}{14}q-\frac{15}{14}.\frac{13}{15}& \text{Uitwerken } \\ & =-pq+\frac{13}{15}p+\frac{15}{14}q-\frac{195}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{13}{15}p+\frac{15}{14}q-\frac{13}{14} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a-\frac{-17}{5})(q-\frac{14}{4})& =(\color{red}{a}+\color{orange}{\frac{17}{5}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{17}{5})} . \color{green}{(q)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{2}a+\frac{17}{5}q-\frac{17}{5}.\frac{7}{2}& \text{Uitwerken } \\ & =aq-\frac{7}{2}a+\frac{17}{5}q-\frac{119}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{-15}{7})(b+\frac{17}{19})& =(\color{red}{x}+\color{orange}{\frac{-15}{7}}).(\color{green}{b}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{19}x-\frac{15}{7}b-\frac{15}{7}.\frac{17}{19}& \text{Uitwerken } \\ & =bx+\frac{17}{19}x-\frac{15}{7}b-\frac{255}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{17}{17})(x-\frac{-3}{6})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}a+1x+1.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}a+1x+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{15}{15})(\frac{6}{18}+p)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{3}p-1p-1.\frac{1}{3}& \text{Uitwerken } \\ & =p^2+(\frac{1}{3}+(-1))p-(\frac{-1}{3}) & \text{Neem samen} \\ &=p^2-\frac{2}{3}p-(\frac{-1}{3}) & \text{Maak de som} \\\end{align}\)