Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(80y^{5}-125y^{3}\)
2. \(75s^{9}-210s^{6}+147s^{3}\)
3. \(-24x^{11}-24x^{8}-6x^{5}\)
4. \(-216s^{18}+294s^{2}\)
5. \(-72b^{5}+98b^{3}\)
6. \(54b^{19}-150b^{5}\)
7. \(32q^{17}-18q^{3}\)
8. \(-108p^{15}+147p^{5}\)
9. \(9s^{9}+24s^{6}+16s^{3}\)
10. \(147x^{8}-126x^{6}+27x^{4}\)
11. \(-48p^{8}-24p^{6}-3p^{4}\)
12. \(-75p^{10}+60p^{6}y-12p^{2}y^2\)

---

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

Verbetersleutel

1. \(80y^{5}-125y^{3}=5y^{3}(16y^{2}-25)=5y^{3}(4y+5)(4y-5)\)
2. \(75s^{9}-210s^{6}+147s^{3}=3s^{3}(25s^{6}-70s^3+49)=3s^{3}(5s^3-7)^2\)
3. \(-24x^{11}-24x^{8}-6x^{5}=-6x^{5}(4x^{6}+4x^3+1)=-6x^{5}(2x^3+1)^2\)
4. \(-216s^{18}+294s^{2}=-6s^{2}(36s^{16}-49)=-6s^{2}(6s^8+7)(6s^8-7)\)
5. \(-72b^{5}+98b^{3}=-2b^{3}(36b^{2}-49)=-2b^{3}(6b+7)(6b-7)\)
6. \(54b^{19}-150b^{5}=6b^{5}(9b^{14}-25)=6b^{5}(3b^7+5)(3b^7-5)\)
7. \(32q^{17}-18q^{3}=2q^{3}(16q^{14}-9)=2q^{3}(4q^7+3)(4q^7-3)\)
8. \(-108p^{15}+147p^{5}=-3p^{5}(36p^{10}-49)=-3p^{5}(6p^5+7)(6p^5-7)\)
9. \(9s^{9}+24s^{6}+16s^{3}=s^{3}(9s^{6}+24s^3+16)=s^{3}(3s^3+4)^2\)
10. \(147x^{8}-126x^{6}+27x^{4}=3x^{4}(49x^{4}-42x^2+9)=3x^{4}(7x^2-3)^2\)
11. \(-48p^{8}-24p^{6}-3p^{4}=-3p^{4}(16p^{4}+8p^2+1)=-3p^{4}(4p^2+1)^2\)
12. \(-75p^{10}+60p^{6}y-12p^{2}y^2=-3p^{2}(25p^{8}-20p^4y+4y^2)=-3p^{2}(5p^4-2y)^2\)