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

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Werk uit en vereenvoudig

1. \((a-\frac{17}{7})(q-\frac{-17}{20})\)
2. \((\frac{15}{9}+x)(b+\frac{-17}{17})\)
3. \((\frac{-6}{19}-a)(a+\frac{-9}{2})\)
4. \((\frac{6}{9}+a)(10-q)\)
5. \((a+\frac{11}{7})(q-\frac{-15}{18})\)
6. \((a-\frac{16}{19})(\frac{18}{12}+q)\)
7. \((b+\frac{1}{4})(b-\frac{9}{17})\)
8. \((x+\frac{12}{7})(\frac{-6}{11}+x)\)
9. \((p-\frac{20}{19})(x+\frac{10}{5})\)
10. \((\frac{4}{7}-b)(\frac{1}{19}+x)\)
11. \((\frac{7}{14}-x)(\frac{-9}{3}-b)\)
12. \((x+\frac{1}{2})(\frac{-3}{17}+b)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{17}{7})(q-\frac{-17}{20})& =(\color{red}{a}+\color{orange}{\frac{-17}{7}}).(\color{green}{q}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{20}a-\frac{17}{7}q-\frac{17}{7}.\frac{17}{20}& \text{Uitwerken } \\ & =aq+\frac{17}{20}a-\frac{17}{7}q-\frac{289}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{15}{9}+x)(b+\frac{-17}{17})& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1x+\frac{5}{3}b-\frac{5}{3}.1& \text{Uitwerken } \\ & =bx-1x+\frac{5}{3}b-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-6}{19}-a)(a+\frac{-9}{2})& =(\color{red}{-a}+\color{orange}{\frac{-6}{19}}).(\color{green}{a}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{9}{2}a-\frac{6}{19}a+\frac{6}{19}.\frac{9}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{9}{2}+(\frac{-6}{19}))a+(\frac{-54}{38}) & \text{Neem samen} \\ &=-a^2+\frac{159}{38}a+(\frac{-54}{38}) & \text{Maak de som} \\ &=-a^2+\frac{159}{38}a+(\frac{-27}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(\frac{6}{9}+a)(10-q)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{-q}+\color{blue}{10})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(10)} + \color{orange}{(\frac{2}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -aq+10a-\frac{2}{3}q+\frac{2}{3}.10& \text{Uitwerken } \\ & =-aq+10a-\frac{2}{3}q+\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a+\frac{11}{7})(q-\frac{-15}{18})& =(\color{red}{a}+\color{orange}{\frac{11}{7}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{11}{7})} . \color{green}{(q)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{6}a+\frac{11}{7}q+\frac{11}{7}.\frac{5}{6}& \text{Uitwerken } \\ & =aq+\frac{5}{6}a+\frac{11}{7}q+\frac{55}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{16}{19})(\frac{18}{12}+q)& =(\color{red}{a}+\color{orange}{\frac{-16}{19}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{2}a-\frac{16}{19}q-\frac{16}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =aq+\frac{3}{2}a-\frac{16}{19}q-\frac{48}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{2}a-\frac{16}{19}q-\frac{24}{19} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b+\frac{1}{4})(b-\frac{9}{17})& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{17}b+\frac{1}{4}b-\frac{1}{4}.\frac{9}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{17})+\frac{1}{4})b-(\frac{-9}{68}) & \text{Neem samen} \\ &=b^2-\frac{19}{68}b-(\frac{-9}{68}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(x+\frac{12}{7})(\frac{-6}{11}+x)& =(\color{red}{x}+\color{orange}{\frac{12}{7}}).(\color{green}{x}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{12}{7})} . \color{green}{(x)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{6}{11}x+\frac{12}{7}x-\frac{12}{7}.\frac{6}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-6}{11})+\frac{12}{7})x-(\frac{-72}{77}) & \text{Neem samen} \\ &=x^2+\frac{90}{77}x-(\frac{-72}{77}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(p-\frac{20}{19})(x+\frac{10}{5})& =(\color{red}{p}+\color{orange}{\frac{-20}{19}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-20}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2p-\frac{20}{19}x-\frac{20}{19}.2& \text{Uitwerken } \\ & =px+2p-\frac{20}{19}x-\frac{40}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{4}{7}-b)(\frac{1}{19}+x)& =(\color{red}{-b}+\color{orange}{\frac{4}{7}}).(\color{green}{x}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{19}b+\frac{4}{7}x+\frac{4}{7}.\frac{1}{19}& \text{Uitwerken } \\ & =-bx-\frac{1}{19}b+\frac{4}{7}x+\frac{4}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{7}{14}-x)(\frac{-9}{3}-b)& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx+3x-\frac{1}{2}b-\frac{1}{2}.3& \text{Uitwerken } \\ & =bx+3x-\frac{1}{2}b-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{1}{2})(\frac{-3}{17}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{17}x+\frac{1}{2}b-\frac{1}{2}.\frac{3}{17}& \text{Uitwerken } \\ & =bx-\frac{3}{17}x+\frac{1}{2}b-\frac{3}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)