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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{11}{5})(\frac{5}{20}-q)& =(\color{red}{x}+\color{orange}{\frac{-11}{5}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{4}x+\frac{11}{5}q-\frac{11}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =-qx+\frac{1}{4}x+\frac{11}{5}q-\frac{11}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{-10}{2})(x+\frac{7}{2})& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{2}b-5x-5.\frac{7}{2}& \text{Uitwerken } \\ & =bx+\frac{7}{2}b-5x-\frac{35}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{-17}{2})(q+\frac{-6}{7})& =(\color{red}{q}+\color{orange}{\frac{17}{2}}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{17}{2})} . \color{green}{(q)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{6}{7}q+\frac{17}{2}q-\frac{17}{2}.\frac{6}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-6}{7})+\frac{17}{2})q-(\frac{-102}{14}) & \text{Neem samen} \\ &=q^2+\frac{107}{14}q-(\frac{-102}{14}) & \text{Maak de som} \\ &=q^2+\frac{107}{14}q+\frac{51}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
4. \(\begin{align}(q-\frac{-16}{4})((-19)+a)& =(\color{red}{q}+\color{orange}{4}).(\color{green}{a}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-19)} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = aq-19q+4a-4.19& \text{Uitwerken } \\ & =aq-19q+4a-76 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{4}{4})(\frac{10}{2}-b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -bx+5x+1b-1.5& \text{Uitwerken } \\ & =-bx+5x+1b-5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-17}{14}+p)(\frac{3}{17}-x)& =(\color{red}{p}+\color{orange}{\frac{-17}{14}}).(\color{green}{-x}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{17}p+\frac{17}{14}x-\frac{17}{14}.\frac{3}{17}& \text{Uitwerken } \\ & =-px+\frac{3}{17}p+\frac{17}{14}x-\frac{51}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{3}{17}p+\frac{17}{14}x-\frac{3}{14} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{-7}{7})(q+\frac{13}{2})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{2}b+1q+1.\frac{13}{2}& \text{Uitwerken } \\ & =bq+\frac{13}{2}b+1q+\frac{13}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-14}{10}+b)(q+\frac{15}{7})& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{q}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{7}b-\frac{7}{5}q-\frac{7}{5}.\frac{15}{7}& \text{Uitwerken } \\ & =bq+\frac{15}{7}b-\frac{7}{5}q-\frac{105}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{15}{7}b-\frac{7}{5}q-3 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p+\frac{16}{18})((-2)+q)& =(\color{red}{p}+\color{orange}{\frac{8}{9}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p+\frac{8}{9}q-\frac{8}{9}.2& \text{Uitwerken } \\ & =pq-2p+\frac{8}{9}q-\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-4)(a+\frac{11}{7})& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{7}x-4a-4.\frac{11}{7}& \text{Uitwerken } \\ & =ax+\frac{11}{7}x-4a-\frac{44}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{-1}{10})(b+\frac{-7}{7})& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a-\frac{1}{10}b+\frac{1}{10}.1& \text{Uitwerken } \\ & =ab-1a-\frac{1}{10}b+\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-6}{7}+b)(b-\frac{19}{2})& =(\color{red}{b}+\color{orange}{\frac{-6}{7}}).(\color{green}{b}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{19}{2}b-\frac{6}{7}b+\frac{6}{7}.\frac{19}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-19}{2})+(\frac{-6}{7}))b+\frac{114}{14} & \text{Neem samen} \\ &=b^2-\frac{145}{14}b+\frac{114}{14} & \text{Maak de som} \\ &=b^2-\frac{145}{14}b+\frac{57}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)