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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-12}{12})(\frac{6}{14}-b)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{7}q-1b+1.\frac{3}{7}& \text{Uitwerken } \\ & =-bq+\frac{3}{7}q-1b+\frac{3}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{14}{2}+x)(b+\frac{6}{6})& =(\color{red}{x}+\color{orange}{7}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(7)} . \color{green}{(b)} + \color{orange}{(7)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+7b+7.1& \text{Uitwerken } \\ & =bx+1x+7b+7 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{11}{15}+q)(a+\frac{-13}{8})& =(\color{red}{q}+\color{orange}{\frac{11}{15}}).(\color{green}{a}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{11}{15})} . \color{green}{(a)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{8}q+\frac{11}{15}a-\frac{11}{15}.\frac{13}{8}& \text{Uitwerken } \\ & =aq-\frac{13}{8}q+\frac{11}{15}a-\frac{143}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{8}{19}+p)(q-\frac{-4}{10})& =(\color{red}{p}+\color{orange}{\frac{8}{19}}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{8}{19})} . \color{green}{(q)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{5}p+\frac{8}{19}q+\frac{8}{19}.\frac{2}{5}& \text{Uitwerken } \\ & =pq+\frac{2}{5}p+\frac{8}{19}q+\frac{16}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{8}{13}+a)(x+\frac{-8}{17})& =(\color{red}{a}+\color{orange}{\frac{8}{13}}).(\color{green}{x}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{8}{13})} . \color{green}{(x)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{17}a+\frac{8}{13}x-\frac{8}{13}.\frac{8}{17}& \text{Uitwerken } \\ & =ax-\frac{8}{17}a+\frac{8}{13}x-\frac{64}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{4}{13}-b)(\frac{-11}{13}+a)& =(\color{red}{-b}+\color{orange}{\frac{4}{13}}).(\color{green}{a}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{4}{13})} . \color{green}{(a)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{13}b+\frac{4}{13}a-\frac{4}{13}.\frac{11}{13}& \text{Uitwerken } \\ & =-ab+\frac{11}{13}b+\frac{4}{13}a-\frac{44}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x-\frac{-5}{6})(b+\frac{-16}{5})& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{b}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{5}x+\frac{5}{6}b-\frac{5}{6}.\frac{16}{5}& \text{Uitwerken } \\ & =bx-\frac{16}{5}x+\frac{5}{6}b-\frac{80}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{16}{5}x+\frac{5}{6}b-\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q+\frac{-7}{15})(\frac{-15}{16}-x)& =(\color{red}{q}+\color{orange}{\frac{-7}{15}}).(\color{green}{-x}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{15}{16}q+\frac{7}{15}x+\frac{7}{15}.\frac{15}{16}& \text{Uitwerken } \\ & =-qx-\frac{15}{16}q+\frac{7}{15}x+\frac{105}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{15}{16}q+\frac{7}{15}x+\frac{7}{16} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-13}{13}+p)(\frac{17}{3}-a)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{3}p+1a-1.\frac{17}{3}& \text{Uitwerken } \\ & =-ap+\frac{17}{3}p+1a-\frac{17}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-18}{11})(x-\frac{6}{10})& =(\color{red}{a}+\color{orange}{\frac{-18}{11}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{5}a-\frac{18}{11}x+\frac{18}{11}.\frac{3}{5}& \text{Uitwerken } \\ & =ax-\frac{3}{5}a-\frac{18}{11}x+\frac{54}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-2}{10}-q)(\frac{17}{9}-p)& =(\color{red}{-q}+\color{orange}{\frac{-1}{5}}).(\color{green}{-p}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{9}q+\frac{1}{5}p-\frac{1}{5}.\frac{17}{9}& \text{Uitwerken } \\ & =pq-\frac{17}{9}q+\frac{1}{5}p-\frac{17}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{10}{20})(\frac{-9}{18}-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{2}q+\frac{1}{2}a+\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq-\frac{1}{2}q+\frac{1}{2}a+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)