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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{3}{18}+p)(\frac{1}{10}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{10}p+\frac{1}{6}a+\frac{1}{6}.\frac{1}{10}& \text{Uitwerken } \\ & =ap+\frac{1}{10}p+\frac{1}{6}a+\frac{1}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{1}{3})(q+\frac{-5}{10})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}b-\frac{1}{3}q+\frac{1}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}b-\frac{1}{3}q+\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(6-q)(p-11)& =(\color{red}{-q}+\color{orange}{6}).(\color{green}{p}+\color{blue}{(-11)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(-11)} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = -pq+11q+6p-6.11& \text{Uitwerken } \\ & =-pq+11q+6p-66 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{4}{13}-x)(p+\frac{20}{7})& =(\color{red}{-x}+\color{orange}{\frac{4}{13}}).(\color{green}{p}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{20}{7}x+\frac{4}{13}p+\frac{4}{13}.\frac{20}{7}& \text{Uitwerken } \\ & =-px-\frac{20}{7}x+\frac{4}{13}p+\frac{80}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{7}{7}-x)(x+\frac{-13}{10})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{10}x+1x-1.\frac{13}{10}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{10}+1)x-\frac{13}{10} & \text{Neem samen} \\ &=-x^2+\frac{23}{10}x-\frac{13}{10} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(b-\frac{4}{5})(\frac{5}{7}+x)& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{7}b-\frac{4}{5}x-\frac{4}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =bx+\frac{5}{7}b-\frac{4}{5}x-\frac{20}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{7}b-\frac{4}{5}x-\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}((-20)+a)(\frac{-17}{15}-b)& =(\color{red}{a}+\color{orange}{(-20)}).(\color{green}{-b}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(-20)} . \color{green}{(-b)} + \color{orange}{(-20)} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{15}a+20b+20.\frac{17}{15}& \text{Uitwerken } \\ & =-ab-\frac{17}{15}a+20b+\frac{340}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{17}{15}a+20b+\frac{68}{3} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{15}{16}-b)(\frac{-17}{9}-b)& =(\color{red}{-b}+\color{orange}{\frac{15}{16}}).(\color{green}{-b}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{15}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{17}{9}b-\frac{15}{16}b-\frac{15}{16}.\frac{17}{9}& \text{Uitwerken } \\ & =b^2+(\frac{17}{9}+(\frac{-15}{16}))b-(\frac{-255}{144}) & \text{Neem samen} \\ &=b^2+\frac{137}{144}b-(\frac{-255}{144}) & \text{Maak de som} \\ &=b^2+\frac{137}{144}b+\frac{85}{48} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(\frac{-13}{6}+a)(\frac{1}{14}+a)& =(\color{red}{a}+\color{orange}{\frac{-13}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{14}a-\frac{13}{6}a-\frac{13}{6}.\frac{1}{14}& \text{Uitwerken } \\ & =a^2+(\frac{1}{14}+(\frac{-13}{6}))a-(\frac{-13}{84}) & \text{Neem samen} \\ &=a^2-\frac{88}{42}a-(\frac{-13}{84}) & \text{Maak de som} \\ &=a^2-\frac{44}{21}a+\frac{13}{84} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
10. \(\begin{align}(\frac{8}{2}+b)(p-\frac{-14}{7})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp+2b+4p+4.2& \text{Uitwerken } \\ & =bp+2b+4p+8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{-12}{6})(\frac{10}{16}+b)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{8}b+2b+2.\frac{5}{8}& \text{Uitwerken } \\ & =b^2+(\frac{5}{8}+2)b+\frac{10}{8} & \text{Neem samen} \\ &=b^2+\frac{21}{8}b+\frac{10}{8} & \text{Maak de som} \\ &=b^2+\frac{21}{8}b+\frac{5}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(a+\frac{-18}{10})(p+\frac{13}{8})& =(\color{red}{a}+\color{orange}{\frac{-9}{5}}).(\color{green}{p}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{8}a-\frac{9}{5}p-\frac{9}{5}.\frac{13}{8}& \text{Uitwerken } \\ & =ap+\frac{13}{8}a-\frac{9}{5}p-\frac{117}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)