Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(2b^{7}+28b^{6}+98b^{5}\)
2. \(-6b^{4}-60b^{3}-150b^{2}\)
3. \(36b^{9}-b^{5}\)
4. \(216y^{16}-150y^{2}\)
5. \(-20p^{10}-20p^{6}y-5p^{2}y^2\)
6. \(72y^{6}-50y^{4}\)
7. \(2q^{5}+36q^{4}+162q^{3}\)
8. \(-192a^{14}+240a^{9}-75a^{4}\)
9. \(48b^{6}-72b^{4}p+27b^{2}p^2\)
10. \(49p^{12}-42p^{7}+9p^{2}\)
11. \(-108p^{7}+3p^{5}\)
12. \(6q^{4}-150q^{2}\)

---

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

Verbetersleutel

1. \(2b^{7}+28b^{6}+98b^{5}=2b^{5}(b^2+14b+49)=2b^{5}(b+7)^2\)
2. \(-6b^{4}-60b^{3}-150b^{2}=-6b^{2}(b^2+10b+25)=-6b^{2}(b+5)^2\)
3. \(36b^{9}-b^{5}=b^{5}(36b^{4}-1)=b^{5}(6b^2+1)(6b^2-1)\)
4. \(216y^{16}-150y^{2}=6y^{2}(36y^{14}-25)=6y^{2}(6y^7+5)(6y^7-5)\)
5. \(-20p^{10}-20p^{6}y-5p^{2}y^2=-5p^{2}(4p^{8}+4p^4y+y^2)=-5p^{2}(2p^4+y)^2\)
6. \(72y^{6}-50y^{4}=2y^{4}(36y^{2}-25)=2y^{4}(6y+5)(6y-5)\)
7. \(2q^{5}+36q^{4}+162q^{3}=2q^{3}(q^2+18q+81)=2q^{3}(q+9)^2\)
8. \(-192a^{14}+240a^{9}-75a^{4}=-3a^{4}(64a^{10}-80a^5+25)=-3a^{4}(8a^5-5)^2\)
9. \(48b^{6}-72b^{4}p+27b^{2}p^2=3b^{2}(16b^{4}-24b^2p+9p^2)=3b^{2}(4b^2-3p)^2\)
10. \(49p^{12}-42p^{7}+9p^{2}=p^{2}(49p^{10}-42p^5+9)=p^{2}(7p^5-3)^2\)
11. \(-108p^{7}+3p^{5}=-3p^{5}(36p^{2}-1)=-3p^{5}(6p+1)(6p-1)\)
12. \(6q^{4}-150q^{2}=6q^{2}(q^2-25)=6q^{2}(q+5)(q-5)\)