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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-19}{16})(\frac{-19}{10}-a)& =(\color{red}{p}+\color{orange}{\frac{19}{16}}).(\color{green}{-a}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{19}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{10}p-\frac{19}{16}a-\frac{19}{16}.\frac{19}{10}& \text{Uitwerken } \\ & =-ap-\frac{19}{10}p-\frac{19}{16}a-\frac{361}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-11}{17})(x+\frac{-16}{18})& =(\color{red}{b}+\color{orange}{\frac{11}{17}}).(\color{green}{x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{11}{17})} . \color{green}{(x)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{8}{9}b+\frac{11}{17}x-\frac{11}{17}.\frac{8}{9}& \text{Uitwerken } \\ & =bx-\frac{8}{9}b+\frac{11}{17}x-\frac{88}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{-9}{6})(\frac{19}{2}-b)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{-b}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{2}a+\frac{3}{2}b-\frac{3}{2}.\frac{19}{2}& \text{Uitwerken } \\ & =-ab+\frac{19}{2}a+\frac{3}{2}b-\frac{57}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-4}{13}-x)(\frac{-13}{10}+p)& =(\color{red}{-x}+\color{orange}{\frac{-4}{13}}).(\color{green}{p}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{10}x-\frac{4}{13}p+\frac{4}{13}.\frac{13}{10}& \text{Uitwerken } \\ & =-px+\frac{13}{10}x-\frac{4}{13}p+\frac{52}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{13}{10}x-\frac{4}{13}p+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(q-9)(\frac{-7}{12}+x)& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{12}q-9x+9.\frac{7}{12}& \text{Uitwerken } \\ & =qx-\frac{7}{12}q-9x+\frac{63}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{7}{12}q-9x+\frac{21}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{5}{20})(b+\frac{-15}{8})& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{15}{8}b+\frac{1}{4}b-\frac{1}{4}.\frac{15}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-15}{8})+\frac{1}{4})b-(\frac{-15}{32}) & \text{Neem samen} \\ &=b^2-\frac{13}{8}b-(\frac{-15}{32}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{18}-b)(\frac{19}{11}-p)& =(\color{red}{-b}+\color{orange}{\frac{-13}{18}}).(\color{green}{-p}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{11}b+\frac{13}{18}p-\frac{13}{18}.\frac{19}{11}& \text{Uitwerken } \\ & =bp-\frac{19}{11}b+\frac{13}{18}p-\frac{247}{198} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{-19}{8})(b-\frac{-11}{7})& =(\color{red}{x}+\color{orange}{\frac{-19}{8}}).(\color{green}{b}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{7}x-\frac{19}{8}b-\frac{19}{8}.\frac{11}{7}& \text{Uitwerken } \\ & =bx+\frac{11}{7}x-\frac{19}{8}b-\frac{209}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{19}{8})(\frac{9}{10}-q)& =(\color{red}{p}+\color{orange}{\frac{19}{8}}).(\color{green}{-q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{19}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{10}p-\frac{19}{8}q+\frac{19}{8}.\frac{9}{10}& \text{Uitwerken } \\ & =-pq+\frac{9}{10}p-\frac{19}{8}q+\frac{171}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-20}{8})(\frac{-6}{10}-p)& =(\color{red}{x}+\color{orange}{\frac{5}{2}}).(\color{green}{-p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{5}x-\frac{5}{2}p-\frac{5}{2}.\frac{3}{5}& \text{Uitwerken } \\ & =-px-\frac{3}{5}x-\frac{5}{2}p-\frac{15}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{3}{5}x-\frac{5}{2}p-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b+\frac{1}{18})(a-\frac{-17}{2})& =(\color{red}{b}+\color{orange}{\frac{1}{18}}).(\color{green}{a}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{1}{18})} . \color{green}{(a)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{2}b+\frac{1}{18}a+\frac{1}{18}.\frac{17}{2}& \text{Uitwerken } \\ & =ab+\frac{17}{2}b+\frac{1}{18}a+\frac{17}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{11}{5})(\frac{-8}{5}+a)& =(\color{red}{b}+\color{orange}{\frac{11}{5}}).(\color{green}{a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{11}{5})} . \color{green}{(a)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{5}b+\frac{11}{5}a-\frac{11}{5}.\frac{8}{5}& \text{Uitwerken } \\ & =ab-\frac{8}{5}b+\frac{11}{5}a-\frac{88}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)