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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{15}+x)(p-\frac{15}{19})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{15}{19}x-1p+1.\frac{15}{19}& \text{Uitwerken } \\ & =px-\frac{15}{19}x-1p+\frac{15}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-4}{12})(x+\frac{-20}{8})& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{2}p+\frac{1}{3}x-\frac{1}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =px-\frac{5}{2}p+\frac{1}{3}x-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{11}{2})((-8)-p)& =(\color{red}{q}+\color{orange}{\frac{-11}{2}}).(\color{green}{-p}+\color{blue}{(-8)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(-8)} + \color{orange}{(\frac{-11}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -pq-8q+\frac{11}{2}p+\frac{11}{2}.8& \text{Uitwerken } \\ & =-pq-8q+\frac{11}{2}p+\frac{88}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-8q+\frac{11}{2}p+44 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b-\frac{7}{17})(a-\frac{-9}{6})& =(\color{red}{b}+\color{orange}{\frac{-7}{17}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{2}b-\frac{7}{17}a-\frac{7}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =ab+\frac{3}{2}b-\frac{7}{17}a-\frac{21}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-12}{5}+b)(x+\frac{-4}{8})& =(\color{red}{b}+\color{orange}{\frac{-12}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}b-\frac{12}{5}x+\frac{12}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}b-\frac{12}{5}x+\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{2}b-\frac{12}{5}x+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-8}{8}-x)(x-5)& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(-5)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -xx+5x-1x+1.5& \text{Uitwerken } \\ & =-x^2+(5+(-1))x+(-5) & \text{Neem samen} \\ &=-x^2+4x+(-5) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(q-\frac{-15}{11})(x-\frac{-18}{16})& =(\color{red}{q}+\color{orange}{\frac{15}{11}}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{15}{11})} . \color{green}{(x)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{8}q+\frac{15}{11}x+\frac{15}{11}.\frac{9}{8}& \text{Uitwerken } \\ & =qx+\frac{9}{8}q+\frac{15}{11}x+\frac{135}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{-15}{18})(\frac{6}{3}+x)& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2a+\frac{5}{6}x+\frac{5}{6}.2& \text{Uitwerken } \\ & =ax+2a+\frac{5}{6}x+\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+2a+\frac{5}{6}x+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a+\frac{8}{2})(x+\frac{18}{6})& =(\color{red}{a}+\color{orange}{4}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ax+3a+4x+4.3& \text{Uitwerken } \\ & =ax+3a+4x+12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{8}{7}+q)(\frac{-5}{16}+b)& =(\color{red}{q}+\color{orange}{\frac{8}{7}}).(\color{green}{b}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{16}q+\frac{8}{7}b-\frac{8}{7}.\frac{5}{16}& \text{Uitwerken } \\ & =bq-\frac{5}{16}q+\frac{8}{7}b-\frac{40}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{16}q+\frac{8}{7}b-\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{13}{3}+x)(p-\frac{5}{4})& =(\color{red}{x}+\color{orange}{\frac{13}{3}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{13}{3})} . \color{green}{(p)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{4}x+\frac{13}{3}p-\frac{13}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =px-\frac{5}{4}x+\frac{13}{3}p-\frac{65}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{-7}{11})(\frac{10}{5}-p)& =(\color{red}{x}+\color{orange}{\frac{-7}{11}}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -px+2x+\frac{7}{11}p-\frac{7}{11}.2& \text{Uitwerken } \\ & =-px+2x+\frac{7}{11}p-\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)