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

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Werk uit en vereenvoudig

1. \((\frac{15}{4}-x)(q-\frac{-2}{19})\)
2. \((\frac{5}{12}+a)(\frac{5}{7}+b)\)
3. \((p+\frac{-4}{17})(p-\frac{-12}{19})\)
4. \((q-\frac{-7}{14})(p+\frac{-20}{20})\)
5. \((\frac{-6}{2}+x)(\frac{-17}{13}+p)\)
6. \((\frac{20}{3}-q)(\frac{-16}{2}+b)\)
7. \((\frac{1}{13}+q)(b+\frac{-17}{7})\)
8. \((b-\frac{5}{12})(\frac{10}{8}+a)\)
9. \((x+\frac{-17}{14})(p+\frac{-2}{9})\)
10. \((x+\frac{-2}{15})(q+\frac{-17}{18})\)
11. \((p+\frac{-16}{7})(\frac{-17}{7}+b)\)
12. \((x-\frac{-3}{3})(\frac{-20}{15}-p)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{4}-x)(q-\frac{-2}{19})& =(\color{red}{-x}+\color{orange}{\frac{15}{4}}).(\color{green}{q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{19}x+\frac{15}{4}q+\frac{15}{4}.\frac{2}{19}& \text{Uitwerken } \\ & =-qx-\frac{2}{19}x+\frac{15}{4}q+\frac{30}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{2}{19}x+\frac{15}{4}q+\frac{15}{38} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{5}{12}+a)(\frac{5}{7}+b)& =(\color{red}{a}+\color{orange}{\frac{5}{12}}).(\color{green}{b}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{5}{12})} . \color{green}{(b)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{7}a+\frac{5}{12}b+\frac{5}{12}.\frac{5}{7}& \text{Uitwerken } \\ & =ab+\frac{5}{7}a+\frac{5}{12}b+\frac{25}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-4}{17})(p-\frac{-12}{19})& =(\color{red}{p}+\color{orange}{\frac{-4}{17}}).(\color{green}{p}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{12}{19}p-\frac{4}{17}p-\frac{4}{17}.\frac{12}{19}& \text{Uitwerken } \\ & =p^2+(\frac{12}{19}+(\frac{-4}{17}))p-(\frac{-48}{323}) & \text{Neem samen} \\ &=p^2+\frac{128}{323}p-(\frac{-48}{323}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(q-\frac{-7}{14})(p+\frac{-20}{20})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q+\frac{1}{2}p-\frac{1}{2}.1& \text{Uitwerken } \\ & =pq-1q+\frac{1}{2}p-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{2}+x)(\frac{-17}{13}+p)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{13}x-3p+3.\frac{17}{13}& \text{Uitwerken } \\ & =px-\frac{17}{13}x-3p+\frac{51}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{20}{3}-q)(\frac{-16}{2}+b)& =(\color{red}{-q}+\color{orange}{\frac{20}{3}}).(\color{green}{b}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-8)} + \color{orange}{(\frac{20}{3})} . \color{green}{(b)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -bq+8q+\frac{20}{3}b-\frac{20}{3}.8& \text{Uitwerken } \\ & =-bq+8q+\frac{20}{3}b-\frac{160}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{1}{13}+q)(b+\frac{-17}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{13}}).(\color{green}{b}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{7}q+\frac{1}{13}b-\frac{1}{13}.\frac{17}{7}& \text{Uitwerken } \\ & =bq-\frac{17}{7}q+\frac{1}{13}b-\frac{17}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{5}{12})(\frac{10}{8}+a)& =(\color{red}{b}+\color{orange}{\frac{-5}{12}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{4}b-\frac{5}{12}a-\frac{5}{12}.\frac{5}{4}& \text{Uitwerken } \\ & =ab+\frac{5}{4}b-\frac{5}{12}a-\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-17}{14})(p+\frac{-2}{9})& =(\color{red}{x}+\color{orange}{\frac{-17}{14}}).(\color{green}{p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{9}x-\frac{17}{14}p+\frac{17}{14}.\frac{2}{9}& \text{Uitwerken } \\ & =px-\frac{2}{9}x-\frac{17}{14}p+\frac{34}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{9}x-\frac{17}{14}p+\frac{17}{63} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x+\frac{-2}{15})(q+\frac{-17}{18})& =(\color{red}{x}+\color{orange}{\frac{-2}{15}}).(\color{green}{q}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{18}x-\frac{2}{15}q+\frac{2}{15}.\frac{17}{18}& \text{Uitwerken } \\ & =qx-\frac{17}{18}x-\frac{2}{15}q+\frac{34}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{17}{18}x-\frac{2}{15}q+\frac{17}{135} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{-16}{7})(\frac{-17}{7}+b)& =(\color{red}{p}+\color{orange}{\frac{-16}{7}}).(\color{green}{b}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{7}p-\frac{16}{7}b+\frac{16}{7}.\frac{17}{7}& \text{Uitwerken } \\ & =bp-\frac{17}{7}p-\frac{16}{7}b+\frac{272}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{-3}{3})(\frac{-20}{15}-p)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{3}x-1p-1.\frac{4}{3}& \text{Uitwerken } \\ & =-px-\frac{4}{3}x-1p-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)