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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{11}+a)(\frac{9}{11}-p)& =(\color{red}{a}+\color{orange}{\frac{-20}{11}}).(\color{green}{-p}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{11}a+\frac{20}{11}p-\frac{20}{11}.\frac{9}{11}& \text{Uitwerken } \\ & =-ap+\frac{9}{11}a+\frac{20}{11}p-\frac{180}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-8}{10})(\frac{-12}{9}+p)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{3}p+\frac{4}{5}p-\frac{4}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{3})+\frac{4}{5})p-(\frac{-16}{15}) & \text{Neem samen} \\ &=p^2-\frac{8}{15}p-(\frac{-16}{15}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(b-\frac{-11}{19})(a+\frac{1}{11})& =(\color{red}{b}+\color{orange}{\frac{11}{19}}).(\color{green}{a}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{11}b+\frac{11}{19}a+\frac{11}{19}.\frac{1}{11}& \text{Uitwerken } \\ & =ab+\frac{1}{11}b+\frac{11}{19}a+\frac{11}{209} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{11}b+\frac{11}{19}a+\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b-\frac{-17}{13})(\frac{12}{7}+p)& =(\color{red}{b}+\color{orange}{\frac{17}{13}}).(\color{green}{p}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{17}{13})} . \color{green}{(p)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{7}b+\frac{17}{13}p+\frac{17}{13}.\frac{12}{7}& \text{Uitwerken } \\ & =bp+\frac{12}{7}b+\frac{17}{13}p+\frac{204}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-14}{16}+x)(x-\frac{-18}{4})& =(\color{red}{x}+\color{orange}{\frac{-7}{8}}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{2}x-\frac{7}{8}x-\frac{7}{8}.\frac{9}{2}& \text{Uitwerken } \\ & =x^2+(\frac{9}{2}+(\frac{-7}{8}))x-(\frac{-63}{16}) & \text{Neem samen} \\ &=x^2+\frac{29}{8}x-(\frac{-63}{16}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-8}{18}-p)((-2)+b)& =(\color{red}{-p}+\color{orange}{\frac{-4}{9}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2p-\frac{4}{9}b+\frac{4}{9}.2& \text{Uitwerken } \\ & =-bp+2p-\frac{4}{9}b+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{15}{10})(a-\frac{13}{15})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{15}q-\frac{3}{2}a+\frac{3}{2}.\frac{13}{15}& \text{Uitwerken } \\ & =aq-\frac{13}{15}q-\frac{3}{2}a+\frac{39}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{13}{15}q-\frac{3}{2}a+\frac{13}{10} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a+\frac{10}{13})(\frac{16}{13}+q)& =(\color{red}{a}+\color{orange}{\frac{10}{13}}).(\color{green}{q}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{13}a+\frac{10}{13}q+\frac{10}{13}.\frac{16}{13}& \text{Uitwerken } \\ & =aq+\frac{16}{13}a+\frac{10}{13}q+\frac{160}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{-17}{6})(12-p)& =(\color{red}{p}+\color{orange}{\frac{17}{6}}).(\color{green}{-p}+\color{blue}{12})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(12)} + \color{orange}{(\frac{17}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -pp+12p-\frac{17}{6}p+\frac{17}{6}.12& \text{Uitwerken } \\ & =-p^2+(12+(\frac{-17}{6}))p+(\frac{-204}{6}) & \text{Neem samen} \\ &=-p^2+\frac{55}{6}p+(\frac{-204}{6}) & \text{Maak de som} \\ &=-p^2+\frac{55}{6}p+(-34) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{9}{2}-a)(\frac{-9}{4}-q)& =(\color{red}{-a}+\color{orange}{\frac{9}{2}}).(\color{green}{-q}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{9}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{4}a-\frac{9}{2}q-\frac{9}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =aq+\frac{9}{4}a-\frac{9}{2}q-\frac{81}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b+\frac{7}{11})(p+\frac{2}{17})& =(\color{red}{b}+\color{orange}{\frac{7}{11}}).(\color{green}{p}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{7}{11})} . \color{green}{(p)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{17}b+\frac{7}{11}p+\frac{7}{11}.\frac{2}{17}& \text{Uitwerken } \\ & =bp+\frac{2}{17}b+\frac{7}{11}p+\frac{14}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{4}{6}+x)(p+\frac{13}{2})& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{2}x+\frac{2}{3}p+\frac{2}{3}.\frac{13}{2}& \text{Uitwerken } \\ & =px+\frac{13}{2}x+\frac{2}{3}p+\frac{26}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{13}{2}x+\frac{2}{3}p+\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)