Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

  1. \((8b^5+12)(8b^5-12)\)
  2. \((14q^3-3)(-14q^3-3)\)
  3. \((5q^2+3b)^2\)
  4. \((-2b+13)(-2b+13)\)
  5. \((x-11)(x+11)\)
  6. \((a+7)^2\)
  7. \((-13q^4-9x)^2\)
  8. \((2p^4+12s)^2\)
  9. \((-7y^3+12)(-7y^3+12)\)
  10. \((-3s^3-12)(-3s^3-12)\)
  11. \((-7q^2-6)^2\)
  12. \((8b^5-10)^2\)

Bereken de volgende merkwaardige producten

Verbetersleutel

  1. \((\color{blue}{8b^5}\color{red}{+12})(\color{blue}{8b^5}\color{red}{-12})=\color{blue}{(8b^5)}^2-\color{red}{12}^2=64b^{10}-144\)
  2. \((\color{red}{14q^3}\color{blue}{-3})(\color{red}{-14q^3}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(14q^3)}^2=9-196q^{6}\)
  3. \((5q^2+3b)^2=(5q^2)^2\color{magenta}{+2.(5q^2).(3b)}+(3b)^2=25q^{4}\color{magenta}{+30bq^2}+9b^2\)
  4. \((-2b+13)(-2b+13)=(-2b+13)^2=(-2b)^2+\color{magenta}{2.(-2b).13}+13^2=4b^2\color{magenta}{-52b}+169\)
  5. \((\color{blue}{x}\color{red}{-11})(\color{blue}{x}\color{red}{+11})=\color{blue}{x}^2-\color{red}{11}^2=x^2-121\)
  6. \((a+7)^2=a^2+\color{magenta}{2.a.7}+7^2=a^2\color{magenta}{+14a}+49\)
  7. \((-13q^4-9x)^2=(-13q^4)^2\color{magenta}{+2.(-13q^4).(-9x)}+(-9x)^2=169q^{8}\color{magenta}{+234q^4x}+81x^2\)
  8. \((2p^4+12s)^2=(2p^4)^2\color{magenta}{+2.(2p^4).(12s)}+(12s)^2=4p^{8}\color{magenta}{+48p^4s}+144s^2\)
  9. \((-7y^3+12)(-7y^3+12)=(-7y^3+12)^2=(-7y^3)^2\color{magenta}{+2.(-7y^3).12}+12^2=49y^{6}\color{magenta}{-168y^3}+144\)
  10. \((-3s^3-12)(-3s^3-12)=(-3s^3-12)^2=(-3s^3)^2\color{magenta}{+2.(-3s^3).(-12)}+(-12)^2=9s^{6}\color{magenta}{+72s^3}+144\)
  11. \((-7q^2-6)^2=(-7q^2)^2\color{magenta}{+2.(-7q^2).(-6)}+(-6)^2=49q^{4}\color{magenta}{+84q^2}+36\)
  12. \((8b^5-10)^2=(8b^5)^2\color{magenta}{+2.(8b^5).(-10)}+(-10)^2=64b^{10}\color{magenta}{-160b^5}+100\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 07:59:03