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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{17}+q)(\frac{19}{3}+a)& =(\color{red}{q}+\color{orange}{\frac{-2}{17}}).(\color{green}{a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{3}q-\frac{2}{17}a-\frac{2}{17}.\frac{19}{3}& \text{Uitwerken } \\ & =aq+\frac{19}{3}q-\frac{2}{17}a-\frac{38}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(1-a)(\frac{7}{19}-b)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{19}a-1b+1.\frac{7}{19}& \text{Uitwerken } \\ & =ab-\frac{7}{19}a-1b+\frac{7}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-17}{14}+b)(x+\frac{11}{13})& =(\color{red}{b}+\color{orange}{\frac{-17}{14}}).(\color{green}{x}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{13}b-\frac{17}{14}x-\frac{17}{14}.\frac{11}{13}& \text{Uitwerken } \\ & =bx+\frac{11}{13}b-\frac{17}{14}x-\frac{187}{182} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{20}{11}-q)(\frac{7}{14}+b)& =(\color{red}{-q}+\color{orange}{\frac{20}{11}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{20}{11})} . \color{green}{(b)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{2}q+\frac{20}{11}b+\frac{20}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =-bq-\frac{1}{2}q+\frac{20}{11}b+\frac{20}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{2}q+\frac{20}{11}b+\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{6}{8}+p)(\frac{-4}{15}+b)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{15}p+\frac{3}{4}b-\frac{3}{4}.\frac{4}{15}& \text{Uitwerken } \\ & =bp-\frac{4}{15}p+\frac{3}{4}b-\frac{12}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{15}p+\frac{3}{4}b-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{7}{14}-q)(b+\frac{-10}{2})& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-5)} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -bq+5q+\frac{1}{2}b-\frac{1}{2}.5& \text{Uitwerken } \\ & =-bq+5q+\frac{1}{2}b-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{12}{4}-a)(\frac{-6}{9}+x)& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{3}a+3x-3.\frac{2}{3}& \text{Uitwerken } \\ & =-ax+\frac{2}{3}a+3x-\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{2}{3}a+3x-2 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{15}{9}-b)(\frac{-20}{7}+a)& =(\color{red}{-b}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{20}{7}b+\frac{5}{3}a-\frac{5}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =-ab+\frac{20}{7}b+\frac{5}{3}a-\frac{100}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{13}{3}+b)(\frac{4}{8}+x)& =(\color{red}{b}+\color{orange}{\frac{13}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{13}{3})} . \color{green}{(x)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}b+\frac{13}{3}x+\frac{13}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}b+\frac{13}{3}x+\frac{13}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{15}{20})(\frac{5}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}b-\frac{3}{4}a-\frac{3}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}b-\frac{3}{4}a-\frac{3}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{3}b-\frac{3}{4}a-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-3}{15}+p)(\frac{19}{4}-x)& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{-x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{4}p+\frac{1}{5}x-\frac{1}{5}.\frac{19}{4}& \text{Uitwerken } \\ & =-px+\frac{19}{4}p+\frac{1}{5}x-\frac{19}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-17}{15})(b+\frac{5}{5})& =(\color{red}{q}+\color{orange}{\frac{17}{15}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{17}{15})} . \color{green}{(b)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q+\frac{17}{15}b+\frac{17}{15}.1& \text{Uitwerken } \\ & =bq+1q+\frac{17}{15}b+\frac{17}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)