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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{18}{8}+a)(\frac{-19}{19}-b)& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{9}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1a-\frac{9}{4}b-\frac{9}{4}.1& \text{Uitwerken } \\ & =-ab-1a-\frac{9}{4}b-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{10}{15}+x)(\frac{-3}{2}+p)& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{2}x+\frac{2}{3}p-\frac{2}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =px-\frac{3}{2}x+\frac{2}{3}p-\frac{6}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{3}{2}x+\frac{2}{3}p-1 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b-\frac{14}{13})(\frac{-12}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{-14}{13}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-14}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bb-1b+\frac{14}{13}b+\frac{14}{13}.1& \text{Uitwerken } \\ & =-b^2+((-1)+\frac{14}{13})b+(\frac{-14}{13}) & \text{Neem samen} \\ &=-b^2+\frac{1}{13}b+(\frac{-14}{13}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{12}{13}-x)(q+\frac{9}{12})& =(\color{red}{-x}+\color{orange}{\frac{12}{13}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{12}{13})} . \color{green}{(q)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{4}x+\frac{12}{13}q+\frac{12}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx-\frac{3}{4}x+\frac{12}{13}q+\frac{36}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{3}{4}x+\frac{12}{13}q+\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{9}{18})(b-\frac{18}{15})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{5}p-\frac{1}{2}b+\frac{1}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =bp-\frac{6}{5}p-\frac{1}{2}b+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{6}{5}p-\frac{1}{2}b+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{1}{2})(\frac{5}{6}-a)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{-a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{6}x+\frac{1}{2}a-\frac{1}{2}.\frac{5}{6}& \text{Uitwerken } \\ & =-ax+\frac{5}{6}x+\frac{1}{2}a-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{5}{16})(a+\frac{-5}{3})& =(\color{red}{q}+\color{orange}{\frac{5}{16}}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{5}{16})} . \color{green}{(a)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{3}q+\frac{5}{16}a-\frac{5}{16}.\frac{5}{3}& \text{Uitwerken } \\ & =aq-\frac{5}{3}q+\frac{5}{16}a-\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{7}{13})(a-\frac{-5}{14})& =(\color{red}{q}+\color{orange}{\frac{-7}{13}}).(\color{green}{a}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{14}q-\frac{7}{13}a-\frac{7}{13}.\frac{5}{14}& \text{Uitwerken } \\ & =aq+\frac{5}{14}q-\frac{7}{13}a-\frac{35}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{14}q-\frac{7}{13}a-\frac{5}{26} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-5}{19}-p)(a-12)& =(\color{red}{-p}+\color{orange}{\frac{-5}{19}}).(\color{green}{a}+\color{blue}{(-12)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-12)} + \color{orange}{(\frac{-5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = -ap+12p-\frac{5}{19}a+\frac{5}{19}.12& \text{Uitwerken } \\ & =-ap+12p-\frac{5}{19}a+\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{-1}{12})(\frac{-7}{13}-x)& =(\color{red}{q}+\color{orange}{\frac{1}{12}}).(\color{green}{-x}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{1}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{13}q-\frac{1}{12}x-\frac{1}{12}.\frac{7}{13}& \text{Uitwerken } \\ & =-qx-\frac{7}{13}q-\frac{1}{12}x-\frac{7}{156} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{19}{19}-b)(\frac{-14}{10}-x)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{5}b-1x-1.\frac{7}{5}& \text{Uitwerken } \\ & =bx+\frac{7}{5}b-1x-\frac{7}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{8}{17})(b-\frac{4}{8})& =(\color{red}{a}+\color{orange}{\frac{-8}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}a-\frac{8}{17}b+\frac{8}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}a-\frac{8}{17}b+\frac{8}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{2}a-\frac{8}{17}b+\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)