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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{10}{11})(a+\frac{-8}{5})& =(\color{red}{p}+\color{orange}{\frac{-10}{11}}).(\color{green}{a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{5}p-\frac{10}{11}a+\frac{10}{11}.\frac{8}{5}& \text{Uitwerken } \\ & =ap-\frac{8}{5}p-\frac{10}{11}a+\frac{80}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{8}{5}p-\frac{10}{11}a+\frac{16}{11} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{9}{3}-p)(q+\frac{-17}{2})& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{2}p+3q-3.\frac{17}{2}& \text{Uitwerken } \\ & =-pq+\frac{17}{2}p+3q-\frac{51}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-14}{4}+x)(p-\frac{-14}{10})& =(\color{red}{x}+\color{orange}{\frac{-7}{2}}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{5}x-\frac{7}{2}p-\frac{7}{2}.\frac{7}{5}& \text{Uitwerken } \\ & =px+\frac{7}{5}x-\frac{7}{2}p-\frac{49}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{2}{16}-q)(\frac{-1}{15}-b)& =(\color{red}{-q}+\color{orange}{\frac{1}{8}}).(\color{green}{-b}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{15}q-\frac{1}{8}b-\frac{1}{8}.\frac{1}{15}& \text{Uitwerken } \\ & =bq+\frac{1}{15}q-\frac{1}{8}b-\frac{1}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{19}{12}-b)(\frac{12}{14}+a)& =(\color{red}{-b}+\color{orange}{\frac{19}{12}}).(\color{green}{a}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{6}{7}b+\frac{19}{12}a+\frac{19}{12}.\frac{6}{7}& \text{Uitwerken } \\ & =-ab-\frac{6}{7}b+\frac{19}{12}a+\frac{114}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{6}{7}b+\frac{19}{12}a+\frac{19}{14} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{-7}{20})(\frac{13}{5}-a)& =(\color{red}{b}+\color{orange}{\frac{-7}{20}}).(\color{green}{-a}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{13}{5}b+\frac{7}{20}a-\frac{7}{20}.\frac{13}{5}& \text{Uitwerken } \\ & =-ab+\frac{13}{5}b+\frac{7}{20}a-\frac{91}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{-10}{10})(q-\frac{-9}{3})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq+3a+1q+1.3& \text{Uitwerken } \\ & =aq+3a+1q+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{-16}{13})(b-\frac{16}{12})& =(\color{red}{p}+\color{orange}{\frac{16}{13}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{16}{13})} . \color{green}{(b)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}p+\frac{16}{13}b-\frac{16}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}p+\frac{16}{13}b-\frac{64}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{7}{20}+x)(b-\frac{-2}{17})& =(\color{red}{x}+\color{orange}{\frac{7}{20}}).(\color{green}{b}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{7}{20})} . \color{green}{(b)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{17}x+\frac{7}{20}b+\frac{7}{20}.\frac{2}{17}& \text{Uitwerken } \\ & =bx+\frac{2}{17}x+\frac{7}{20}b+\frac{14}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{2}{17}x+\frac{7}{20}b+\frac{7}{170} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{-3}{19})(p-(-3))& =(\color{red}{q}+\color{orange}{\frac{-3}{19}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-3}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pq+3q-\frac{3}{19}p-\frac{3}{19}.3& \text{Uitwerken } \\ & =pq+3q-\frac{3}{19}p-\frac{9}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-20}{17}+q)(\frac{7}{15}+b)& =(\color{red}{q}+\color{orange}{\frac{-20}{17}}).(\color{green}{b}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{15}q-\frac{20}{17}b-\frac{20}{17}.\frac{7}{15}& \text{Uitwerken } \\ & =bq+\frac{7}{15}q-\frac{20}{17}b-\frac{140}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{15}q-\frac{20}{17}b-\frac{28}{51} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(b+\frac{-10}{10})(b+\frac{-3}{9})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{3}b-1b+1.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{3})+(-1))b+\frac{1}{3} & \text{Neem samen} \\ &=b^2-\frac{4}{3}b+\frac{1}{3} & \text{Maak de som} \\\end{align}\)