Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-20b^{13}+245b^{3}\)
2. \(27q^{15}+18q^{10}y+3q^{5}y^2\)
3. \(9b^{13}-30b^{8}+25b^{3}\)
4. \(-32b^{12}-80b^{7}s-50b^{2}s^2\)
5. \(-16y^{8}+24y^{6}-9y^{4}\)
6. \(-48a^{10}-72a^{7}y-27a^{4}y^2\)
7. \(125b^{4}-200b^{3}+80b^{2}\)
8. \(-50y^{7}+2y^{5}\)
9. \(8s^{4}+8s^{3}+2s^{2}\)
10. \(80p^{6}-280p^{5}+245p^{4}\)
11. \(-6x^{5}+72x^{4}-216x^{3}\)
12. \(-s^{5}-18s^{4}-81s^{3}\)

---

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

Verbetersleutel

1. \(-20b^{13}+245b^{3}=-5b^{3}(4b^{10}-49)=-5b^{3}(2b^5+7)(2b^5-7)\)
2. \(27q^{15}+18q^{10}y+3q^{5}y^2=3q^{5}(9q^{10}+6q^5y+y^2)=3q^{5}(3q^5+y)^2\)
3. \(9b^{13}-30b^{8}+25b^{3}=b^{3}(9b^{10}-30b^5+25)=b^{3}(3b^5-5)^2\)
4. \(-32b^{12}-80b^{7}s-50b^{2}s^2=-2b^{2}(16b^{10}+40b^5s+25s^2)=-2b^{2}(4b^5+5s)^2\)
5. \(-16y^{8}+24y^{6}-9y^{4}=-y^{4}(16y^{4}-24y^2+9)=-y^{4}(4y^2-3)^2\)
6. \(-48a^{10}-72a^{7}y-27a^{4}y^2=-3a^{4}(16a^{6}+24a^3y+9y^2)=-3a^{4}(4a^3+3y)^2\)
7. \(125b^{4}-200b^{3}+80b^{2}=5b^{2}(25b^{2}-40b+16)=5b^{2}(5b-4)^2\)
8. \(-50y^{7}+2y^{5}=-2y^{5}(25y^{2}-1)=-2y^{5}(5y+1)(5y-1)\)
9. \(8s^{4}+8s^{3}+2s^{2}=2s^{2}(4s^{2}+4s+1)=2s^{2}(2s+1)^2\)
10. \(80p^{6}-280p^{5}+245p^{4}=5p^{4}(16p^{2}-56p+49)=5p^{4}(4p-7)^2\)
11. \(-6x^{5}+72x^{4}-216x^{3}=-6x^{3}(x^2-12x+36)=-6x^{3}(x-6)^2\)
12. \(-s^{5}-18s^{4}-81s^{3}=-s^{3}(s^2+18s+81)=-s^{3}(s+9)^2\)