Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-5p^{4}+20p^{2}\)
2. \(-320a^{9}-80a^{7}s-5a^{5}s^2\)
3. \(-75a^{13}+120a^{9}q-48a^{5}q^2\)
4. \(-64p^{6}-16p^{5}-p^{4}\)
5. \(4b^{19}-25b^{3}\)
6. \(-5s^{5}+5s^{3}\)
7. \(25a^{13}+20a^{8}b+4a^{3}b^2\)
8. \(-180q^{7}+125q^{5}\)
9. \(-96q^{7}+54q^{5}\)
10. \(-3p^{7}+108p^{5}\)
11. \(245q^{11}-140q^{7}+20q^{3}\)
12. \(-80s^{5}+120s^{4}-45s^{3}\)

---

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

Verbetersleutel

1. \(-5p^{4}+20p^{2}=-5p^{2}(p^2-4)=-5p^{2}(p+2)(p-2)\)
2. \(-320a^{9}-80a^{7}s-5a^{5}s^2=-5a^{5}(64a^{4}+16a^2s+s^2)=-5a^{5}(8a^2+s)^2\)
3. \(-75a^{13}+120a^{9}q-48a^{5}q^2=-3a^{5}(25a^{8}-40a^4q+16q^2)=-3a^{5}(5a^4-4q)^2\)
4. \(-64p^{6}-16p^{5}-p^{4}=-p^{4}(64p^{2}+16p+1)=-p^{4}(8p+1)^2\)
5. \(4b^{19}-25b^{3}=b^{3}(4b^{16}-25)=b^{3}(2b^8+5)(2b^8-5)\)
6. \(-5s^{5}+5s^{3}=-5s^{3}(s^2-1)=-5s^{3}(s-1)(s+1)\)
7. \(25a^{13}+20a^{8}b+4a^{3}b^2=a^{3}(25a^{10}+20a^5b+4b^2)=a^{3}(5a^5+2b)^2\)
8. \(-180q^{7}+125q^{5}=-5q^{5}(36q^{2}-25)=-5q^{5}(6q+5)(6q-5)\)
9. \(-96q^{7}+54q^{5}=-6q^{5}(16q^{2}-9)=-6q^{5}(4q+3)(4q-3)\)
10. \(-3p^{7}+108p^{5}=-3p^{5}(p^2-36)=-3p^{5}(p+6)(p-6)\)
11. \(245q^{11}-140q^{7}+20q^{3}=5q^{3}(49q^{8}-28q^4+4)=5q^{3}(7q^4-2)^2\)
12. \(-80s^{5}+120s^{4}-45s^{3}=-5s^{3}(16s^{2}-24s+9)=-5s^{3}(4s-3)^2\)