Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(20p^{6}+100p^{5}+125p^{4}\)
2. \(-147y^{8}+252y^{5}-108y^{2}\)
3. \(54a^{5}+144a^{4}+96a^{3}\)
4. \(-320b^{12}+560b^{8}-245b^{4}\)
5. \(-6q^{6}+150q^{4}\)
6. \(192a^{11}-336a^{7}q+147a^{3}q^2\)
7. \(20y^{5}-5y^{3}\)
8. \(-8b^{7}+18b^{5}\)
9. \(-72b^{5}+2b^{3}\)
10. \(32b^{6}-98b^{4}\)
11. \(-36b^{7}-12b^{6}-b^{5}\)
12. \(-5q^{4}-10q^{3}-5q^{2}\)

---

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

Verbetersleutel

1. \(20p^{6}+100p^{5}+125p^{4}=5p^{4}(4p^{2}+20p+25)=5p^{4}(2p+5)^2\)
2. \(-147y^{8}+252y^{5}-108y^{2}=-3y^{2}(49y^{6}-84y^3+36)=-3y^{2}(7y^3-6)^2\)
3. \(54a^{5}+144a^{4}+96a^{3}=6a^{3}(9a^{2}+24a+16)=6a^{3}(3a+4)^2\)
4. \(-320b^{12}+560b^{8}-245b^{4}=-5b^{4}(64b^{8}-112b^4+49)=-5b^{4}(8b^4-7)^2\)
5. \(-6q^{6}+150q^{4}=-6q^{4}(q^2-25)=-6q^{4}(q+5)(q-5)\)
6. \(192a^{11}-336a^{7}q+147a^{3}q^2=3a^{3}(64a^{8}-112a^4q+49q^2)=3a^{3}(8a^4-7q)^2\)
7. \(20y^{5}-5y^{3}=5y^{3}(4y^{2}-1)=5y^{3}(2y+1)(2y-1)\)
8. \(-8b^{7}+18b^{5}=-2b^{5}(4b^{2}-9)=-2b^{5}(2b+3)(2b-3)\)
9. \(-72b^{5}+2b^{3}=-2b^{3}(36b^{2}-1)=-2b^{3}(6b+1)(6b-1)\)
10. \(32b^{6}-98b^{4}=2b^{4}(16b^{2}-49)=2b^{4}(4b+7)(4b-7)\)
11. \(-36b^{7}-12b^{6}-b^{5}=-b^{5}(36b^{2}+12b+1)=-b^{5}(6b+1)^2\)
12. \(-5q^{4}-10q^{3}-5q^{2}=-5q^{2}(q^2+2q+1)=-5q^{2}(q+1)^2\)