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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{10}+b)(b+\frac{9}{12})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{4}b-\frac{1}{2}b-\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =b^2+(\frac{3}{4}+(\frac{-1}{2}))b-(\frac{-3}{8}) & \text{Neem samen} \\ &=b^2+\frac{1}{4}b-(\frac{-3}{8}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{11}{7}+b)(\frac{9}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{11}{7}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{11}{7})} . \color{green}{(a)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{4}b+\frac{11}{7}a+\frac{11}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =ab+\frac{3}{4}b+\frac{11}{7}a+\frac{33}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{3}{6})(a+\frac{20}{17})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{17}q-\frac{1}{2}a-\frac{1}{2}.\frac{20}{17}& \text{Uitwerken } \\ & =aq+\frac{20}{17}q-\frac{1}{2}a-\frac{20}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{20}{17}q-\frac{1}{2}a-\frac{10}{17} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{17}{11}+q)(x-\frac{-11}{5})& =(\color{red}{q}+\color{orange}{\frac{17}{11}}).(\color{green}{x}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{17}{11})} . \color{green}{(x)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{5}q+\frac{17}{11}x+\frac{17}{11}.\frac{11}{5}& \text{Uitwerken } \\ & =qx+\frac{11}{5}q+\frac{17}{11}x+\frac{187}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{11}{5}q+\frac{17}{11}x+\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}((-5)+x)(\frac{12}{19}+q)& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{19}x-5q-5.\frac{12}{19}& \text{Uitwerken } \\ & =qx+\frac{12}{19}x-5q-\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{7}{16}+q)(p-\frac{-14}{2})& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{p}+\color{blue}{7})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(7)} + \color{orange}{(\frac{7}{16})} . \color{green}{(p)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = pq+7q+\frac{7}{16}p+\frac{7}{16}.7& \text{Uitwerken } \\ & =pq+7q+\frac{7}{16}p+\frac{49}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{11}{11})(p+\frac{14}{19})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{14}{19}p+1p+1.\frac{14}{19}& \text{Uitwerken } \\ & =p^2+(\frac{14}{19}+1)p+\frac{14}{19} & \text{Neem samen} \\ &=p^2+\frac{33}{19}p+\frac{14}{19} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(b-\frac{-16}{7})(a+\frac{1}{16})& =(\color{red}{b}+\color{orange}{\frac{16}{7}}).(\color{green}{a}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{16}{7})} . \color{green}{(a)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{16}b+\frac{16}{7}a+\frac{16}{7}.\frac{1}{16}& \text{Uitwerken } \\ & =ab+\frac{1}{16}b+\frac{16}{7}a+\frac{16}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{16}b+\frac{16}{7}a+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(b+\frac{10}{12})(2-b)& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{-b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bb+2b-\frac{5}{6}b+\frac{5}{6}.2& \text{Uitwerken } \\ & =-b^2+(2+(\frac{-5}{6}))b+(\frac{-10}{6}) & \text{Neem samen} \\ &=-b^2+\frac{7}{6}b+(\frac{-10}{6}) & \text{Maak de som} \\ &=-b^2+\frac{7}{6}b+(\frac{-5}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{-9}{17}+b)(q-\frac{9}{3})& =(\color{red}{b}+\color{orange}{\frac{-9}{17}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-9}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bq-3b-\frac{9}{17}q+\frac{9}{17}.3& \text{Uitwerken } \\ & =bq-3b-\frac{9}{17}q+\frac{27}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-15}{11})(a+\frac{-10}{4})& =(\color{red}{p}+\color{orange}{\frac{-15}{11}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{2}p-\frac{15}{11}a+\frac{15}{11}.\frac{5}{2}& \text{Uitwerken } \\ & =ap-\frac{5}{2}p-\frac{15}{11}a+\frac{75}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-3}{16})((-5)-p)& =(\color{red}{q}+\color{orange}{\frac{3}{16}}).(\color{green}{-p}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{3}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -pq-5q-\frac{3}{16}p-\frac{3}{16}.5& \text{Uitwerken } \\ & =-pq-5q-\frac{3}{16}p-\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)