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

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1. \((p-\frac{-7}{14})(\frac{-17}{14}-q)\)
2. \((q-\frac{-6}{20})(q+\frac{-1}{8})\)
3. \((\frac{9}{16}-q)(\frac{-15}{5}-a)\)
4. \((\frac{-9}{3}+a)(\frac{17}{14}-p)\)
5. \((x+\frac{2}{14})(q+\frac{-13}{7})\)
6. \((x-\frac{-2}{4})(q+\frac{5}{3})\)
7. \((a+\frac{15}{2})(q-\frac{-10}{7})\)
8. \((a+\frac{13}{15})(p+\frac{-17}{5})\)
9. \((\frac{6}{6}-x)(\frac{3}{3}-x)\)
10. \((x+\frac{-6}{6})(\frac{3}{17}-p)\)
11. \((\frac{18}{16}+p)(a-\frac{1}{7})\)
12. \((a+\frac{6}{11})(\frac{13}{17}+p)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-7}{14})(\frac{-17}{14}-q)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{17}{14}p-\frac{1}{2}q-\frac{1}{2}.\frac{17}{14}& \text{Uitwerken } \\ & =-pq-\frac{17}{14}p-\frac{1}{2}q-\frac{17}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{-6}{20})(q+\frac{-1}{8})& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{8}q+\frac{3}{10}q-\frac{3}{10}.\frac{1}{8}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{8})+\frac{3}{10})q-(\frac{-3}{80}) & \text{Neem samen} \\ &=q^2+\frac{7}{40}q-(\frac{-3}{80}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{9}{16}-q)(\frac{-15}{5}-a)& =(\color{red}{-q}+\color{orange}{\frac{9}{16}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(-3)} + \color{orange}{(\frac{9}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = aq+3q-\frac{9}{16}a-\frac{9}{16}.3& \text{Uitwerken } \\ & =aq+3q-\frac{9}{16}a-\frac{27}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-9}{3}+a)(\frac{17}{14}-p)& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{-p}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(-3)} . \color{green}{(-p)} + \color{orange}{(-3)} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{14}a+3p-3.\frac{17}{14}& \text{Uitwerken } \\ & =-ap+\frac{17}{14}a+3p-\frac{51}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{2}{14})(q+\frac{-13}{7})& =(\color{red}{x}+\color{orange}{\frac{1}{7}}).(\color{green}{q}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{7}x+\frac{1}{7}q-\frac{1}{7}.\frac{13}{7}& \text{Uitwerken } \\ & =qx-\frac{13}{7}x+\frac{1}{7}q-\frac{13}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{-2}{4})(q+\frac{5}{3})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{3}x+\frac{1}{2}q+\frac{1}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =qx+\frac{5}{3}x+\frac{1}{2}q+\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{15}{2})(q-\frac{-10}{7})& =(\color{red}{a}+\color{orange}{\frac{15}{2}}).(\color{green}{q}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{7}a+\frac{15}{2}q+\frac{15}{2}.\frac{10}{7}& \text{Uitwerken } \\ & =aq+\frac{10}{7}a+\frac{15}{2}q+\frac{150}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{7}a+\frac{15}{2}q+\frac{75}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a+\frac{13}{15})(p+\frac{-17}{5})& =(\color{red}{a}+\color{orange}{\frac{13}{15}}).(\color{green}{p}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{13}{15})} . \color{green}{(p)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{5}a+\frac{13}{15}p-\frac{13}{15}.\frac{17}{5}& \text{Uitwerken } \\ & =ap-\frac{17}{5}a+\frac{13}{15}p-\frac{221}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{6}{6}-x)(\frac{3}{3}-x)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x-1x+1.1& \text{Uitwerken } \\ & =x^2+((-1)+(-1))x+1 & \text{Neem samen} \\ &=x^2-2x+1 & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(x+\frac{-6}{6})(\frac{3}{17}-p)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{17}x+1p-1.\frac{3}{17}& \text{Uitwerken } \\ & =-px+\frac{3}{17}x+1p-\frac{3}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{18}{16}+p)(a-\frac{1}{7})& =(\color{red}{p}+\color{orange}{\frac{9}{8}}).(\color{green}{a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{7}p+\frac{9}{8}a-\frac{9}{8}.\frac{1}{7}& \text{Uitwerken } \\ & =ap-\frac{1}{7}p+\frac{9}{8}a-\frac{9}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a+\frac{6}{11})(\frac{13}{17}+p)& =(\color{red}{a}+\color{orange}{\frac{6}{11}}).(\color{green}{p}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{6}{11})} . \color{green}{(p)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{17}a+\frac{6}{11}p+\frac{6}{11}.\frac{13}{17}& \text{Uitwerken } \\ & =ap+\frac{13}{17}a+\frac{6}{11}p+\frac{78}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)