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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{3}{2}-x)(p+\frac{1}{4})& =(\color{red}{-x}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{4}x+\frac{3}{2}p+\frac{3}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =-px-\frac{1}{4}x+\frac{3}{2}p+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{7}{15}-a)(\frac{4}{13}-q)& =(\color{red}{-a}+\color{orange}{\frac{7}{15}}).(\color{green}{-q}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{7}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{13}a-\frac{7}{15}q+\frac{7}{15}.\frac{4}{13}& \text{Uitwerken } \\ & =aq-\frac{4}{13}a-\frac{7}{15}q+\frac{28}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{19}{14})(b-\frac{4}{4})& =(\color{red}{a}+\color{orange}{\frac{19}{14}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{14})} . \color{green}{(b)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a+\frac{19}{14}b-\frac{19}{14}.1& \text{Uitwerken } \\ & =ab-1a+\frac{19}{14}b-\frac{19}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-17}{13}-b)(\frac{-3}{7}+a)& =(\color{red}{-b}+\color{orange}{\frac{-17}{13}}).(\color{green}{a}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{7}b-\frac{17}{13}a+\frac{17}{13}.\frac{3}{7}& \text{Uitwerken } \\ & =-ab+\frac{3}{7}b-\frac{17}{13}a+\frac{51}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{13}{2})(p+\frac{18}{5})& =(\color{red}{q}+\color{orange}{\frac{13}{2}}).(\color{green}{p}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{13}{2})} . \color{green}{(p)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{5}q+\frac{13}{2}p+\frac{13}{2}.\frac{18}{5}& \text{Uitwerken } \\ & =pq+\frac{18}{5}q+\frac{13}{2}p+\frac{234}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{18}{5}q+\frac{13}{2}p+\frac{117}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+15)(p+\frac{-10}{4})& =(\color{red}{b}+\color{orange}{15}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(15)} . \color{green}{(p)} + \color{orange}{(15)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{2}b+15p-15.\frac{5}{2}& \text{Uitwerken } \\ & =bp-\frac{5}{2}b+15p-\frac{75}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{10}{14})(\frac{-1}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{20}a-\frac{5}{7}a+\frac{5}{7}.\frac{1}{20}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{20})+(\frac{-5}{7}))a+\frac{5}{140} & \text{Neem samen} \\ &=a^2-\frac{107}{140}a+\frac{5}{140} & \text{Maak de som} \\ &=a^2-\frac{107}{140}a+\frac{1}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(a-\frac{-3}{2})(b-\frac{-4}{13})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{13}a+\frac{3}{2}b+\frac{3}{2}.\frac{4}{13}& \text{Uitwerken } \\ & =ab+\frac{4}{13}a+\frac{3}{2}b+\frac{12}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{4}{13}a+\frac{3}{2}b+\frac{6}{13} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{6}{8}+q)(\frac{-5}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{-q}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{5}{19}q-\frac{3}{4}q-\frac{3}{4}.\frac{5}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-5}{19})+(\frac{-3}{4}))q-\frac{15}{76} & \text{Neem samen} \\ &=-q^2-\frac{77}{76}q-\frac{15}{76} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}((-2)-a)(\frac{-6}{17}+p)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{6}{17}a-2p+2.\frac{6}{17}& \text{Uitwerken } \\ & =-ap+\frac{6}{17}a-2p+\frac{12}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{18}{15})(p+\frac{2}{16})& =(\color{red}{q}+\color{orange}{\frac{-6}{5}}).(\color{green}{p}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{8}q-\frac{6}{5}p-\frac{6}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =pq+\frac{1}{8}q-\frac{6}{5}p-\frac{6}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{8}q-\frac{6}{5}p-\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(b+\frac{-3}{11})(\frac{20}{5}-p)& =(\color{red}{b}+\color{orange}{\frac{-3}{11}}).(\color{green}{-p}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{-3}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -bp+4b+\frac{3}{11}p-\frac{3}{11}.4& \text{Uitwerken } \\ & =-bp+4b+\frac{3}{11}p-\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)