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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{4}-x)(p+\frac{2}{10})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{5}x-\frac{1}{2}p-\frac{1}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =-px-\frac{1}{5}x-\frac{1}{2}p-\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{-2}{9})(q-\frac{-15}{16})& =(\color{red}{q}+\color{orange}{\frac{-2}{9}}).(\color{green}{q}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{15}{16}q-\frac{2}{9}q-\frac{2}{9}.\frac{15}{16}& \text{Uitwerken } \\ & =q^2+(\frac{15}{16}+(\frac{-2}{9}))q-(\frac{-30}{144}) & \text{Neem samen} \\ &=q^2+\frac{103}{144}q-(\frac{-30}{144}) & \text{Maak de som} \\ &=q^2+\frac{103}{144}q+\frac{5}{24} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
3. \(\begin{align}(b+\frac{14}{9})(q+\frac{-11}{13})& =(\color{red}{b}+\color{orange}{\frac{14}{9}}).(\color{green}{q}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{14}{9})} . \color{green}{(q)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{13}b+\frac{14}{9}q-\frac{14}{9}.\frac{11}{13}& \text{Uitwerken } \\ & =bq-\frac{11}{13}b+\frac{14}{9}q-\frac{154}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-7}{8}+b)(\frac{11}{8}-a)& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{-a}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{8}b+\frac{7}{8}a-\frac{7}{8}.\frac{11}{8}& \text{Uitwerken } \\ & =-ab+\frac{11}{8}b+\frac{7}{8}a-\frac{77}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{2}{19})(p-\frac{-17}{3})& =(\color{red}{x}+\color{orange}{\frac{-2}{19}}).(\color{green}{p}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{3}x-\frac{2}{19}p-\frac{2}{19}.\frac{17}{3}& \text{Uitwerken } \\ & =px+\frac{17}{3}x-\frac{2}{19}p-\frac{34}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{10}{8})(a-\frac{-17}{14})& =(\color{red}{b}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{14}b-\frac{5}{4}a-\frac{5}{4}.\frac{17}{14}& \text{Uitwerken } \\ & =ab+\frac{17}{14}b-\frac{5}{4}a-\frac{85}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{15}+b)(b+\frac{3}{14})& =(\color{red}{b}+\color{orange}{\frac{-14}{15}}).(\color{green}{b}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{14}b-\frac{14}{15}b-\frac{14}{15}.\frac{3}{14}& \text{Uitwerken } \\ & =b^2+(\frac{3}{14}+(\frac{-14}{15}))b-(\frac{-42}{210}) & \text{Neem samen} \\ &=b^2-\frac{151}{210}b-(\frac{-42}{210}) & \text{Maak de som} \\ &=b^2-\frac{151}{210}b+\frac{1}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(\frac{15}{19}-a)(a-\frac{-18}{19})& =(\color{red}{-a}+\color{orange}{\frac{15}{19}}).(\color{green}{a}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{15}{19})} . \color{green}{(a)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{18}{19}a+\frac{15}{19}a+\frac{15}{19}.\frac{18}{19}& \text{Uitwerken } \\ & =-a^2+((\frac{-18}{19})+\frac{15}{19})a+(\frac{-270}{361}) & \text{Neem samen} \\ &=-a^2-\frac{3}{19}a+(\frac{-270}{361}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(p+\frac{7}{14})(\frac{13}{4}+x)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{4}p+\frac{1}{2}x+\frac{1}{2}.\frac{13}{4}& \text{Uitwerken } \\ & =px+\frac{13}{4}p+\frac{1}{2}x+\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}((-4)+p)(a+\frac{11}{3})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{3}p-4a-4.\frac{11}{3}& \text{Uitwerken } \\ & =ap+\frac{11}{3}p-4a-\frac{44}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{15}{2}-q)(\frac{-1}{11}+a)& =(\color{red}{-q}+\color{orange}{\frac{15}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{15}{2})} . \color{green}{(a)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{11}q+\frac{15}{2}a-\frac{15}{2}.\frac{1}{11}& \text{Uitwerken } \\ & =-aq+\frac{1}{11}q+\frac{15}{2}a-\frac{15}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{7}{7}+x)(q-\frac{-7}{3})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{3}x+1q+1.\frac{7}{3}& \text{Uitwerken } \\ & =qx+\frac{7}{3}x+1q+\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)