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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{16}-x)(\frac{11}{5}+q)& =(\color{red}{-x}+\color{orange}{\frac{15}{16}}).(\color{green}{q}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{5}x+\frac{15}{16}q+\frac{15}{16}.\frac{11}{5}& \text{Uitwerken } \\ & =-qx-\frac{11}{5}x+\frac{15}{16}q+\frac{165}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{11}{5}x+\frac{15}{16}q+\frac{33}{16} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-20}{18}+p)(5-b)& =(\color{red}{p}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -bp+5p+\frac{10}{9}b-\frac{10}{9}.5& \text{Uitwerken } \\ & =-bp+5p+\frac{10}{9}b-\frac{50}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-7}{4}-b)(p+\frac{-12}{8})& =(\color{red}{-b}+\color{orange}{\frac{-7}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{2}b-\frac{7}{4}p+\frac{7}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =-bp+\frac{3}{2}b-\frac{7}{4}p+\frac{21}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{-14}{14})(\frac{-20}{19}-a)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{20}{19}p+1a+1.\frac{20}{19}& \text{Uitwerken } \\ & =-ap-\frac{20}{19}p+1a+\frac{20}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{4}{12}-b)(\frac{-8}{11}-a)& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{-a}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{11}b-\frac{1}{3}a-\frac{1}{3}.\frac{8}{11}& \text{Uitwerken } \\ & =ab+\frac{8}{11}b-\frac{1}{3}a-\frac{8}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{-15}{11})(\frac{9}{6}+p)& =(\color{red}{b}+\color{orange}{\frac{-15}{11}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{2}b-\frac{15}{11}p-\frac{15}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =bp+\frac{3}{2}b-\frac{15}{11}p-\frac{45}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-3}{18}+p)(\frac{-12}{4}-a)& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -ap-3p+\frac{1}{6}a+\frac{1}{6}.3& \text{Uitwerken } \\ & =-ap-3p+\frac{1}{6}a+\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-3p+\frac{1}{6}a+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b+\frac{-7}{10})(p-\frac{-9}{8})& =(\color{red}{b}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{8}b-\frac{7}{10}p-\frac{7}{10}.\frac{9}{8}& \text{Uitwerken } \\ & =bp+\frac{9}{8}b-\frac{7}{10}p-\frac{63}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{16}{11}+p)(\frac{5}{5}+q)& =(\color{red}{p}+\color{orange}{\frac{16}{11}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p+\frac{16}{11}q+\frac{16}{11}.1& \text{Uitwerken } \\ & =pq+1p+\frac{16}{11}q+\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{16}{15})(\frac{-1}{19}-b)& =(\color{red}{b}+\color{orange}{\frac{-16}{15}}).(\color{green}{-b}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{19}b+\frac{16}{15}b+\frac{16}{15}.\frac{1}{19}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{19})+\frac{16}{15})b+(\frac{-16}{285}) & \text{Neem samen} \\ &=-b^2+\frac{289}{285}b+(\frac{-16}{285}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(x+\frac{2}{11})(b+\frac{-4}{15})& =(\color{red}{x}+\color{orange}{\frac{2}{11}}).(\color{green}{b}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{15}x+\frac{2}{11}b-\frac{2}{11}.\frac{4}{15}& \text{Uitwerken } \\ & =bx-\frac{4}{15}x+\frac{2}{11}b-\frac{8}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{-13}{2})(q+\frac{-12}{3})& =(\color{red}{a}+\color{orange}{\frac{13}{2}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{13}{2})} . \color{green}{(q)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4a+\frac{13}{2}q-\frac{13}{2}.4& \text{Uitwerken } \\ & =aq-4a+\frac{13}{2}q-\frac{52}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-4a+\frac{13}{2}q-26 & \text{Vereenvoudig} \\\end{align}\)