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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-4}{2}-a)(\frac{-5}{10}+p)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}a-2p+2.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}a-2p+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{1}{2}a-2p+1 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p+\frac{15}{18})(\frac{17}{17}-x)& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px+1p-\frac{5}{6}x+\frac{5}{6}.1& \text{Uitwerken } \\ & =-px+1p-\frac{5}{6}x+\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-11}{18}-p)(\frac{19}{5}+q)& =(\color{red}{-p}+\color{orange}{\frac{-11}{18}}).(\color{green}{q}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{5}p-\frac{11}{18}q-\frac{11}{18}.\frac{19}{5}& \text{Uitwerken } \\ & =-pq-\frac{19}{5}p-\frac{11}{18}q-\frac{209}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{6}{4})((-20)-q)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{-q}+\color{blue}{(-20)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-20)} + \color{orange}{(\frac{3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -aq-20a-\frac{3}{2}q-\frac{3}{2}.20& \text{Uitwerken } \\ & =-aq-20a-\frac{3}{2}q-\frac{60}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-20a-\frac{3}{2}q-30 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a-\frac{2}{10})(b-\frac{1}{11})& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{11}a-\frac{1}{5}b+\frac{1}{5}.\frac{1}{11}& \text{Uitwerken } \\ & =ab-\frac{1}{11}a-\frac{1}{5}b+\frac{1}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{16}{4})(p-\frac{-2}{3})& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}b-4p-4.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}b-4p-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{-12}{19})(\frac{14}{5}-b)& =(\color{red}{a}+\color{orange}{\frac{-12}{19}}).(\color{green}{-b}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{14}{5}a+\frac{12}{19}b-\frac{12}{19}.\frac{14}{5}& \text{Uitwerken } \\ & =-ab+\frac{14}{5}a+\frac{12}{19}b-\frac{168}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{-14}{10})(\frac{10}{5}-b)& =(\color{red}{p}+\color{orange}{\frac{7}{5}}).(\color{green}{-b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2p-\frac{7}{5}b+\frac{7}{5}.2& \text{Uitwerken } \\ & =-bp+2p-\frac{7}{5}b+\frac{14}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-13}{8}-p)(a-\frac{-5}{9})& =(\color{red}{-p}+\color{orange}{\frac{-13}{8}}).(\color{green}{a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{9}p-\frac{13}{8}a-\frac{13}{8}.\frac{5}{9}& \text{Uitwerken } \\ & =-ap-\frac{5}{9}p-\frac{13}{8}a-\frac{65}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{9}{6}+q)(a-\frac{2}{4})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{2}q+\frac{3}{2}a-\frac{3}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =aq-\frac{1}{2}q+\frac{3}{2}a-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{11}{3}-x)(a-\frac{14}{9})& =(\color{red}{-x}+\color{orange}{\frac{11}{3}}).(\color{green}{a}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{11}{3})} . \color{green}{(a)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{14}{9}x+\frac{11}{3}a-\frac{11}{3}.\frac{14}{9}& \text{Uitwerken } \\ & =-ax+\frac{14}{9}x+\frac{11}{3}a-\frac{154}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-3}{6}-b)(q+\frac{-19}{8})& =(\color{red}{-b}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{19}{8}b-\frac{1}{2}q+\frac{1}{2}.\frac{19}{8}& \text{Uitwerken } \\ & =-bq+\frac{19}{8}b-\frac{1}{2}q+\frac{19}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)