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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{7}+a)(q+\frac{17}{13})& =(\color{red}{a}+\color{orange}{\frac{15}{7}}).(\color{green}{q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{15}{7})} . \color{green}{(q)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{13}a+\frac{15}{7}q+\frac{15}{7}.\frac{17}{13}& \text{Uitwerken } \\ & =aq+\frac{17}{13}a+\frac{15}{7}q+\frac{255}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{5}{10})(\frac{8}{2}+x)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bx+4b-\frac{1}{2}x-\frac{1}{2}.4& \text{Uitwerken } \\ & =bx+4b-\frac{1}{2}x-\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+4b-\frac{1}{2}x-2 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{-6}{12})(a+\frac{9}{9})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1x+\frac{1}{2}a+\frac{1}{2}.1& \text{Uitwerken } \\ & =ax+1x+\frac{1}{2}a+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{-7}{19})(\frac{-6}{11}+b)& =(\color{red}{p}+\color{orange}{\frac{7}{19}}).(\color{green}{b}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{11}p+\frac{7}{19}b-\frac{7}{19}.\frac{6}{11}& \text{Uitwerken } \\ & =bp-\frac{6}{11}p+\frac{7}{19}b-\frac{42}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p-\frac{7}{10})(\frac{18}{17}-p)& =(\color{red}{p}+\color{orange}{\frac{-7}{10}}).(\color{green}{-p}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{18}{17}p+\frac{7}{10}p-\frac{7}{10}.\frac{18}{17}& \text{Uitwerken } \\ & =-p^2+(\frac{18}{17}+\frac{7}{10})p-\frac{126}{170} & \text{Neem samen} \\ &=-p^2+\frac{299}{170}p-\frac{126}{170} & \text{Maak de som} \\ &=-p^2+\frac{299}{170}p-\frac{63}{85} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(\frac{-10}{7}-x)(\frac{-7}{20}+a)& =(\color{red}{-x}+\color{orange}{\frac{-10}{7}}).(\color{green}{a}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{20}x-\frac{10}{7}a+\frac{10}{7}.\frac{7}{20}& \text{Uitwerken } \\ & =-ax+\frac{7}{20}x-\frac{10}{7}a+\frac{70}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{7}{20}x-\frac{10}{7}a+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{7}-x)(\frac{-13}{6}-q)& =(\color{red}{-x}+\color{orange}{\frac{-13}{7}}).(\color{green}{-q}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{6}x+\frac{13}{7}q+\frac{13}{7}.\frac{13}{6}& \text{Uitwerken } \\ & =qx+\frac{13}{6}x+\frac{13}{7}q+\frac{169}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{14}{13}+x)(x-\frac{-4}{3})& =(\color{red}{x}+\color{orange}{\frac{14}{13}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{4}{3}x+\frac{14}{13}x+\frac{14}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =x^2+(\frac{4}{3}+\frac{14}{13})x+\frac{56}{39} & \text{Neem samen} \\ &=x^2+\frac{94}{39}x+\frac{56}{39} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(a+\frac{14}{10})(\frac{-6}{13}-b)& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{-b}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{6}{13}a-\frac{7}{5}b-\frac{7}{5}.\frac{6}{13}& \text{Uitwerken } \\ & =-ab-\frac{6}{13}a-\frac{7}{5}b-\frac{42}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{15}{8}-a)(\frac{-7}{13}+q)& =(\color{red}{-a}+\color{orange}{\frac{15}{8}}).(\color{green}{q}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{15}{8})} . \color{green}{(q)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{13}a+\frac{15}{8}q-\frac{15}{8}.\frac{7}{13}& \text{Uitwerken } \\ & =-aq+\frac{7}{13}a+\frac{15}{8}q-\frac{105}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{6}{3})(\frac{-13}{5}-x)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-x}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(-2)} . \color{green}{(-x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{5}q+2x+2.\frac{13}{5}& \text{Uitwerken } \\ & =-qx-\frac{13}{5}q+2x+\frac{26}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{6}{12})(q+\frac{15}{20})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{4}x+\frac{1}{2}q+\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =qx+\frac{3}{4}x+\frac{1}{2}q+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)