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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{10}{5}+a)(p-\frac{-9}{12})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}a+2p+2.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}a+2p+\frac{6}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{4}a+2p+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-4}{16}+a)(q-\frac{-20}{12})& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{3}a-\frac{1}{4}q-\frac{1}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =aq+\frac{5}{3}a-\frac{1}{4}q-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{15}{16}+q)(\frac{-10}{20}+q)& =(\color{red}{q}+\color{orange}{\frac{15}{16}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{2}q+\frac{15}{16}q-\frac{15}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{2})+\frac{15}{16})q-(\frac{-15}{32}) & \text{Neem samen} \\ &=q^2+\frac{7}{16}q-(\frac{-15}{32}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{2}+p)(x-\frac{-5}{12})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{12}p-1x-1.\frac{5}{12}& \text{Uitwerken } \\ & =px+\frac{5}{12}p-1x-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{-12}{15})(\frac{-4}{19}-p)& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{-p}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{19}b+\frac{4}{5}p+\frac{4}{5}.\frac{4}{19}& \text{Uitwerken } \\ & =-bp-\frac{4}{19}b+\frac{4}{5}p+\frac{16}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{-2}{3})(a-\frac{4}{3})& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{3}q-\frac{2}{3}a+\frac{2}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =aq-\frac{4}{3}q-\frac{2}{3}a+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{14}{2}+q)(\frac{-4}{16}-p)& =(\color{red}{q}+\color{orange}{7}).(\color{green}{-p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(7)} . \color{green}{(-p)} + \color{orange}{(7)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{4}q-7p-7.\frac{1}{4}& \text{Uitwerken } \\ & =-pq-\frac{1}{4}q-7p-\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{12}{15}-x)(\frac{12}{19}+b)& =(\color{red}{-x}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{12}{19}x+\frac{4}{5}b+\frac{4}{5}.\frac{12}{19}& \text{Uitwerken } \\ & =-bx-\frac{12}{19}x+\frac{4}{5}b+\frac{48}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-19}{13})(b-\frac{-6}{20})& =(\color{red}{x}+\color{orange}{\frac{-19}{13}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{10}x-\frac{19}{13}b-\frac{19}{13}.\frac{3}{10}& \text{Uitwerken } \\ & =bx+\frac{3}{10}x-\frac{19}{13}b-\frac{57}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{6}{4})(b+\frac{17}{15})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{15}a+\frac{3}{2}b+\frac{3}{2}.\frac{17}{15}& \text{Uitwerken } \\ & =ab+\frac{17}{15}a+\frac{3}{2}b+\frac{51}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{17}{15}a+\frac{3}{2}b+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}((-4)+a)(p+\frac{8}{11})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{11}a-4p-4.\frac{8}{11}& \text{Uitwerken } \\ & =ap+\frac{8}{11}a-4p-\frac{32}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{-10}{4})(x-\frac{-4}{12})& =(\color{red}{x}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{3}x+\frac{5}{2}x+\frac{5}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =x^2+(\frac{1}{3}+\frac{5}{2})x+\frac{5}{6} & \text{Neem samen} \\ &=x^2+\frac{17}{6}x+\frac{5}{6} & \text{Maak de som} \\\end{align}\)