Ontbinden in factoren (2)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

  1. \(2a^{7}-128a^{5}\)
  2. \(18y^{12}-128y^{4}\)
  3. \(16s^{14}+56s^{9}+49s^{4}\)
  4. \(5s^{4}-50s^{3}+125s^{2}\)
  5. \(6q^{7}-48q^{6}+96q^{5}\)
  6. \(a^{7}-6a^{6}+9a^{5}\)
  7. \(-147s^{10}-252s^{6}y-108s^{2}y^2\)
  8. \(50y^{18}-72y^{4}\)
  9. \(-96x^{7}+294x^{5}\)
  10. \(-8b^{12}+50b^{4}\)
  11. \(-80y^{4}+280y^{3}-245y^{2}\)
  12. \(-3s^{5}+12s^{4}-12s^{3}\)

Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

Verbetersleutel

  1. \(2a^{7}-128a^{5}=2a^{5}(a^2-64)=2a^{5}(a-8)(a+8)\)
  2. \(18y^{12}-128y^{4}=2y^{4}(9y^{8}-64)=2y^{4}(3y^4+8)(3y^4-8)\)
  3. \(16s^{14}+56s^{9}+49s^{4}=s^{4}(16s^{10}+56s^5+49)=s^{4}(4s^5+7)^2\)
  4. \(5s^{4}-50s^{3}+125s^{2}=5s^{2}(s^2-10s+25)=5s^{2}(s-5)^2\)
  5. \(6q^{7}-48q^{6}+96q^{5}=6q^{5}(q^2-8q+16)=6q^{5}(q-4)^2\)
  6. \(a^{7}-6a^{6}+9a^{5}=a^{5}(a^2-6a+9)=a^{5}(a-3)^2\)
  7. \(-147s^{10}-252s^{6}y-108s^{2}y^2=-3s^{2}(49s^{8}+84s^4y+36y^2)=-3s^{2}(7s^4+6y)^2\)
  8. \(50y^{18}-72y^{4}=2y^{4}(25y^{14}-36)=2y^{4}(5y^7+6)(5y^7-6)\)
  9. \(-96x^{7}+294x^{5}=-6x^{5}(16x^{2}-49)=-6x^{5}(4x+7)(4x-7)\)
  10. \(-8b^{12}+50b^{4}=-2b^{4}(4b^{8}-25)=-2b^{4}(2b^4+5)(2b^4-5)\)
  11. \(-80y^{4}+280y^{3}-245y^{2}=-5y^{2}(16y^{2}-56y+49)=-5y^{2}(4y-7)^2\)
  12. \(-3s^{5}+12s^{4}-12s^{3}=-3s^{3}(s^2-4s+4)=-3s^{3}(s-2)^2\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 01:22:41