Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(8y^{6}-50y^{4}\)
2. \(-150p^{8}-360p^{5}s-216p^{2}s^2\)
3. \(-32a^{6}+18a^{4}\)
4. \(-216p^{13}-360p^{9}x-150p^{5}x^2\)
5. \(49x^{7}-84x^{6}+36x^{5}\)
6. \(45y^{18}-125y^{4}\)
7. \(-216a^{6}-72a^{5}-6a^{4}\)
8. \(245s^{11}+70s^{7}+5s^{3}\)
9. \(-27a^{15}+3a^{5}\)
10. \(-147s^{7}+378s^{6}-243s^{5}\)
11. \(25x^{15}-4x^{5}\)
12. \(-294p^{8}-420p^{5}q-150p^{2}q^2\)

---

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

Verbetersleutel

1. \(8y^{6}-50y^{4}=2y^{4}(4y^{2}-25)=2y^{4}(2y+5)(2y-5)\)
2. \(-150p^{8}-360p^{5}s-216p^{2}s^2=-6p^{2}(25p^{6}+60p^3s+36s^2)=-6p^{2}(5p^3+6s)^2\)
3. \(-32a^{6}+18a^{4}=-2a^{4}(16a^{2}-9)=-2a^{4}(4a+3)(4a-3)\)
4. \(-216p^{13}-360p^{9}x-150p^{5}x^2=-6p^{5}(36p^{8}+60p^4x+25x^2)=-6p^{5}(6p^4+5x)^2\)
5. \(49x^{7}-84x^{6}+36x^{5}=x^{5}(49x^{2}-84x+36)=x^{5}(7x-6)^2\)
6. \(45y^{18}-125y^{4}=5y^{4}(9y^{14}-25)=5y^{4}(3y^7+5)(3y^7-5)\)
7. \(-216a^{6}-72a^{5}-6a^{4}=-6a^{4}(36a^{2}+12a+1)=-6a^{4}(6a+1)^2\)
8. \(245s^{11}+70s^{7}+5s^{3}=5s^{3}(49s^{8}+14s^4+1)=5s^{3}(7s^4+1)^2\)
9. \(-27a^{15}+3a^{5}=-3a^{5}(9a^{10}-1)=-3a^{5}(3a^5+1)(3a^5-1)\)
10. \(-147s^{7}+378s^{6}-243s^{5}=-3s^{5}(49s^{2}-126s+81)=-3s^{5}(7s-9)^2\)
11. \(25x^{15}-4x^{5}=x^{5}(25x^{10}-4)=x^{5}(5x^5+2)(5x^5-2)\)
12. \(-294p^{8}-420p^{5}q-150p^{2}q^2=-6p^{2}(49p^{6}+70p^3q+25q^2)=-6p^{2}(7p^3+5q)^2\)