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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-17}{5})(\frac{1}{7}-b)& =(\color{red}{a}+\color{orange}{\frac{-17}{5}}).(\color{green}{-b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{7}a+\frac{17}{5}b-\frac{17}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =-ab+\frac{1}{7}a+\frac{17}{5}b-\frac{17}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{15}{7}+x)(\frac{-10}{19}+p)& =(\color{red}{x}+\color{orange}{\frac{15}{7}}).(\color{green}{p}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{19}x+\frac{15}{7}p-\frac{15}{7}.\frac{10}{19}& \text{Uitwerken } \\ & =px-\frac{10}{19}x+\frac{15}{7}p-\frac{150}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{15}{13})(\frac{2}{13}-b)& =(\color{red}{q}+\color{orange}{\frac{15}{13}}).(\color{green}{-b}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{15}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{13}q-\frac{15}{13}b+\frac{15}{13}.\frac{2}{13}& \text{Uitwerken } \\ & =-bq+\frac{2}{13}q-\frac{15}{13}b+\frac{30}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b+\frac{9}{18})(b+\frac{20}{16})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{4}b+\frac{1}{2}b+\frac{1}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =b^2+(\frac{5}{4}+\frac{1}{2})b+\frac{5}{8} & \text{Neem samen} \\ &=b^2+\frac{7}{4}b+\frac{5}{8} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{3}+x)(x-\frac{3}{17})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{17}x-2x+2.\frac{3}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{17})+(-2))x+\frac{6}{17} & \text{Neem samen} \\ &=x^2-\frac{37}{17}x+\frac{6}{17} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{12}{14}+p)(q+(-20))& =(\color{red}{p}+\color{orange}{\frac{6}{7}}).(\color{green}{q}+\color{blue}{(-20)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-20)} + \color{orange}{(\frac{6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = pq-20p+\frac{6}{7}q-\frac{6}{7}.20& \text{Uitwerken } \\ & =pq-20p+\frac{6}{7}q-\frac{120}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{9}{6})(q-\frac{-11}{7})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{7}b+\frac{3}{2}q+\frac{3}{2}.\frac{11}{7}& \text{Uitwerken } \\ & =bq+\frac{11}{7}b+\frac{3}{2}q+\frac{33}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x-\frac{-9}{4})(\frac{-10}{17}-x)& =(\color{red}{x}+\color{orange}{\frac{9}{4}}).(\color{green}{-x}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{10}{17}x-\frac{9}{4}x-\frac{9}{4}.\frac{10}{17}& \text{Uitwerken } \\ & =-x^2+((\frac{-10}{17})+(\frac{-9}{4}))x-\frac{90}{68} & \text{Neem samen} \\ &=-x^2-\frac{193}{68}x-\frac{90}{68} & \text{Maak de som} \\ &=-x^2-\frac{193}{68}x-\frac{45}{34} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(p+\frac{-17}{19})(\frac{-12}{13}+b)& =(\color{red}{p}+\color{orange}{\frac{-17}{19}}).(\color{green}{b}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{12}{13}p-\frac{17}{19}b+\frac{17}{19}.\frac{12}{13}& \text{Uitwerken } \\ & =bp-\frac{12}{13}p-\frac{17}{19}b+\frac{204}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{-8}{16})(\frac{9}{9}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p+\frac{1}{2}a+\frac{1}{2}.1& \text{Uitwerken } \\ & =ap+1p+\frac{1}{2}a+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{5}{13})(\frac{7}{17}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{13}}).(\color{green}{b}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{17}p-\frac{5}{13}b-\frac{5}{13}.\frac{7}{17}& \text{Uitwerken } \\ & =bp+\frac{7}{17}p-\frac{5}{13}b-\frac{35}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{7}{11})(\frac{18}{3}-a)& =(\color{red}{a}+\color{orange}{\frac{-7}{11}}).(\color{green}{-a}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -aa+6a+\frac{7}{11}a-\frac{7}{11}.6& \text{Uitwerken } \\ & =-a^2+(6+\frac{7}{11})a-\frac{42}{11} & \text{Neem samen} \\ &=-a^2+\frac{73}{11}a-\frac{42}{11} & \text{Maak de som} \\\end{align}\)