Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-18a^{7}+50a^{3}\)
2. \(-18q^{8}+2q^{2}\)
3. \(108p^{4}+36p^{3}+3p^{2}\)
4. \(32y^{4}-50y^{2}\)
5. \(192a^{6}+48a^{5}+3a^{4}\)
6. \(5a^{4}-90a^{3}+405a^{2}\)
7. \(-2p^{5}-24p^{4}-72p^{3}\)
8. \(54s^{4}+36s^{3}+6s^{2}\)
9. \(128p^{14}-224p^{9}x+98p^{4}x^2\)
10. \(6p^{7}-84p^{6}+294p^{5}\)
11. \(72s^{11}-50s^{3}\)
12. \(-18y^{9}-48y^{6}-32y^{3}\)

---

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

Verbetersleutel

1. \(-18a^{7}+50a^{3}=-2a^{3}(9a^{4}-25)=-2a^{3}(3a^2+5)(3a^2-5)\)
2. \(-18q^{8}+2q^{2}=-2q^{2}(9q^{6}-1)=-2q^{2}(3q^3+1)(3q^3-1)\)
3. \(108p^{4}+36p^{3}+3p^{2}=3p^{2}(36p^{2}+12p+1)=3p^{2}(6p+1)^2\)
4. \(32y^{4}-50y^{2}=2y^{2}(16y^{2}-25)=2y^{2}(4y+5)(4y-5)\)
5. \(192a^{6}+48a^{5}+3a^{4}=3a^{4}(64a^{2}+16a+1)=3a^{4}(8a+1)^2\)
6. \(5a^{4}-90a^{3}+405a^{2}=5a^{2}(a^2-18a+81)=5a^{2}(a-9)^2\)
7. \(-2p^{5}-24p^{4}-72p^{3}=-2p^{3}(p^2+12p+36)=-2p^{3}(p+6)^2\)
8. \(54s^{4}+36s^{3}+6s^{2}=6s^{2}(9s^{2}+6s+1)=6s^{2}(3s+1)^2\)
9. \(128p^{14}-224p^{9}x+98p^{4}x^2=2p^{4}(64p^{10}-112p^5x+49x^2)=2p^{4}(8p^5-7x)^2\)
10. \(6p^{7}-84p^{6}+294p^{5}=6p^{5}(p^2-14p+49)=6p^{5}(p-7)^2\)
11. \(72s^{11}-50s^{3}=2s^{3}(36s^{8}-25)=2s^{3}(6s^4+5)(6s^4-5)\)
12. \(-18y^{9}-48y^{6}-32y^{3}=-2y^{3}(9y^{6}+24y^3+16)=-2y^{3}(3y^3+4)^2\)