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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{14}-b)(\frac{16}{15}-q)& =(\color{red}{-b}+\color{orange}{\frac{15}{14}}).(\color{green}{-q}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{15}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{15}b-\frac{15}{14}q+\frac{15}{14}.\frac{16}{15}& \text{Uitwerken } \\ & =bq-\frac{16}{15}b-\frac{15}{14}q+\frac{240}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{16}{15}b-\frac{15}{14}q+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b-\frac{-13}{8})(\frac{-15}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{13}{8}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1b-\frac{13}{8}p-\frac{13}{8}.1& \text{Uitwerken } \\ & =-bp-1b-\frac{13}{8}p-\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{10}{7}-b)(\frac{-14}{3}+a)& =(\color{red}{-b}+\color{orange}{\frac{10}{7}}).(\color{green}{a}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{14}{3}b+\frac{10}{7}a-\frac{10}{7}.\frac{14}{3}& \text{Uitwerken } \\ & =-ab+\frac{14}{3}b+\frac{10}{7}a-\frac{140}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{14}{3}b+\frac{10}{7}a-\frac{20}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(q-\frac{-20}{5})(a-\frac{18}{2})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{a}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-9)} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = aq-9q+4a-4.9& \text{Uitwerken } \\ & =aq-9q+4a-36 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{19}{7}+b)(q+\frac{-9}{5})& =(\color{red}{b}+\color{orange}{\frac{19}{7}}).(\color{green}{q}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{19}{7})} . \color{green}{(q)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{5}b+\frac{19}{7}q-\frac{19}{7}.\frac{9}{5}& \text{Uitwerken } \\ & =bq-\frac{9}{5}b+\frac{19}{7}q-\frac{171}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{12}{4}+p)(p-\frac{5}{17})& =(\color{red}{p}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{17}p+3p-3.\frac{5}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{17})+3)p-(\frac{-15}{17}) & \text{Neem samen} \\ &=p^2+\frac{46}{17}p-(\frac{-15}{17}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(b+\frac{-3}{3})(\frac{12}{8}+x)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}b-1x-1.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}b-1x-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{14}{15}+a)(a-\frac{-17}{5})& =(\color{red}{a}+\color{orange}{\frac{14}{15}}).(\color{green}{a}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{14}{15})} . \color{green}{(a)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{17}{5}a+\frac{14}{15}a+\frac{14}{15}.\frac{17}{5}& \text{Uitwerken } \\ & =a^2+(\frac{17}{5}+\frac{14}{15})a+\frac{238}{75} & \text{Neem samen} \\ &=a^2+\frac{65}{15}a+\frac{238}{75} & \text{Maak de som} \\ &=a^2+\frac{13}{3}a+\frac{238}{75} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(\frac{9}{19}+p)(b+\frac{18}{5})& =(\color{red}{p}+\color{orange}{\frac{9}{19}}).(\color{green}{b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{9}{19})} . \color{green}{(b)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{5}p+\frac{9}{19}b+\frac{9}{19}.\frac{18}{5}& \text{Uitwerken } \\ & =bp+\frac{18}{5}p+\frac{9}{19}b+\frac{162}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{18}{7}-q)(p+\frac{-20}{2})& =(\color{red}{-q}+\color{orange}{\frac{18}{7}}).(\color{green}{p}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(-10)} + \color{orange}{(\frac{18}{7})} . \color{green}{(p)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -pq+10q+\frac{18}{7}p-\frac{18}{7}.10& \text{Uitwerken } \\ & =-pq+10q+\frac{18}{7}p-\frac{180}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{5}{18})(p-\frac{-19}{19})& =(\color{red}{p}+\color{orange}{\frac{5}{18}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{18})} . \color{green}{(p)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pp+1p+\frac{5}{18}p+\frac{5}{18}.1& \text{Uitwerken } \\ & =p^2+(1+\frac{5}{18})p+\frac{5}{18} & \text{Neem samen} \\ &=p^2+\frac{23}{18}p+\frac{5}{18} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{4}{19}+a)(q-\frac{-15}{17})& =(\color{red}{a}+\color{orange}{\frac{4}{19}}).(\color{green}{q}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{4}{19})} . \color{green}{(q)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{17}a+\frac{4}{19}q+\frac{4}{19}.\frac{15}{17}& \text{Uitwerken } \\ & =aq+\frac{15}{17}a+\frac{4}{19}q+\frac{60}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)