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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-20}{18})(\frac{1}{2}+p)& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}b-\frac{10}{9}p-\frac{10}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}b-\frac{10}{9}p-\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{2}b-\frac{10}{9}p-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{18}{7}-b)(\frac{-2}{11}-p)& =(\color{red}{-b}+\color{orange}{\frac{18}{7}}).(\color{green}{-p}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{18}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{11}b-\frac{18}{7}p-\frac{18}{7}.\frac{2}{11}& \text{Uitwerken } \\ & =bp+\frac{2}{11}b-\frac{18}{7}p-\frac{36}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{9}{15})(q-\frac{-10}{8})& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{4}p-\frac{3}{5}q-\frac{3}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =pq+\frac{5}{4}p-\frac{3}{5}q-\frac{15}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{4}p-\frac{3}{5}q-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-12}{19}+b)(p+\frac{19}{3})& =(\color{red}{b}+\color{orange}{\frac{-12}{19}}).(\color{green}{p}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{3}b-\frac{12}{19}p-\frac{12}{19}.\frac{19}{3}& \text{Uitwerken } \\ & =bp+\frac{19}{3}b-\frac{12}{19}p-\frac{228}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{3}b-\frac{12}{19}p-4 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-9}{13}-b)(q-\frac{15}{10})& =(\color{red}{-b}+\color{orange}{\frac{-9}{13}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{2}b-\frac{9}{13}q+\frac{9}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq+\frac{3}{2}b-\frac{9}{13}q+\frac{27}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q-\frac{20}{12})(b+\frac{7}{8})& =(\color{red}{q}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{8}q-\frac{5}{3}b-\frac{5}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =bq+\frac{7}{8}q-\frac{5}{3}b-\frac{35}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{6}{5})(a+\frac{19}{20})& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{a}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{20}p+\frac{6}{5}a+\frac{6}{5}.\frac{19}{20}& \text{Uitwerken } \\ & =ap+\frac{19}{20}p+\frac{6}{5}a+\frac{114}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{19}{20}p+\frac{6}{5}a+\frac{57}{50} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a-\frac{-3}{3})(\frac{-7}{14}-a)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{2}a-1a-1.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{2})+(-1))a-\frac{1}{2} & \text{Neem samen} \\ &=-a^2-\frac{3}{2}a-\frac{1}{2} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(q-\frac{-3}{6})(a-\frac{-18}{4})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{2}q+\frac{1}{2}a+\frac{1}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =aq+\frac{9}{2}q+\frac{1}{2}a+\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{4}{6})(p-\frac{7}{6})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{6}b-\frac{2}{3}p+\frac{2}{3}.\frac{7}{6}& \text{Uitwerken } \\ & =bp-\frac{7}{6}b-\frac{2}{3}p+\frac{14}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{6}b-\frac{2}{3}p+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{6}-b)(\frac{15}{18}+x)& =(\color{red}{-b}+\color{orange}{\frac{-7}{6}}).(\color{green}{x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{6}b-\frac{7}{6}x-\frac{7}{6}.\frac{5}{6}& \text{Uitwerken } \\ & =-bx-\frac{5}{6}b-\frac{7}{6}x-\frac{35}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{4}{15})(q-\frac{17}{17})& =(\color{red}{b}+\color{orange}{\frac{-4}{15}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b-\frac{4}{15}q+\frac{4}{15}.1& \text{Uitwerken } \\ & =bq-1b-\frac{4}{15}q+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)