Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-32b^{15}+48b^{10}-18b^{5}\)
2. \(6a^{7}+84a^{6}+294a^{5}\)
3. \(96a^{5}+48a^{4}+6a^{3}\)
4. \(18p^{4}+48p^{3}+32p^{2}\)
5. \(-125b^{5}+45b^{3}\)
6. \(36y^{4}-25y^{2}\)
7. \(-36s^{8}-60s^{6}x-25s^{4}x^2\)
8. \(-80y^{13}-120y^{8}-45y^{3}\)
9. \(-294a^{8}+252a^{6}-54a^{4}\)
10. \(-54b^{10}-180b^{7}p-150b^{4}p^2\)
11. \(-150s^{4}+420s^{3}-294s^{2}\)
12. \(5s^{7}+40s^{6}+80s^{5}\)

---

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

Verbetersleutel

1. \(-32b^{15}+48b^{10}-18b^{5}=-2b^{5}(16b^{10}-24b^5+9)=-2b^{5}(4b^5-3)^2\)
2. \(6a^{7}+84a^{6}+294a^{5}=6a^{5}(a^2+14a+49)=6a^{5}(a+7)^2\)
3. \(96a^{5}+48a^{4}+6a^{3}=6a^{3}(16a^{2}+8a+1)=6a^{3}(4a+1)^2\)
4. \(18p^{4}+48p^{3}+32p^{2}=2p^{2}(9p^{2}+24p+16)=2p^{2}(3p+4)^2\)
5. \(-125b^{5}+45b^{3}=-5b^{3}(25b^{2}-9)=-5b^{3}(5b+3)(5b-3)\)
6. \(36y^{4}-25y^{2}=y^{2}(36y^{2}-25)=y^{2}(6y+5)(6y-5)\)
7. \(-36s^{8}-60s^{6}x-25s^{4}x^2=-s^{4}(36s^{4}+60s^2x+25x^2)=-s^{4}(6s^2+5x)^2\)
8. \(-80y^{13}-120y^{8}-45y^{3}=-5y^{3}(16y^{10}+24y^5+9)=-5y^{3}(4y^5+3)^2\)
9. \(-294a^{8}+252a^{6}-54a^{4}=-6a^{4}(49a^{4}-42a^2+9)=-6a^{4}(7a^2-3)^2\)
10. \(-54b^{10}-180b^{7}p-150b^{4}p^2=-6b^{4}(9b^{6}+30b^3p+25p^2)=-6b^{4}(3b^3+5p)^2\)
11. \(-150s^{4}+420s^{3}-294s^{2}=-6s^{2}(25s^{2}-70s+49)=-6s^{2}(5s-7)^2\)
12. \(5s^{7}+40s^{6}+80s^{5}=5s^{5}(s^2+8s+16)=5s^{5}(s+4)^2\)