Ontbinden in factoren (2)

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

1. \(-6p^{4}-36p^{3}-54p^{2}\)
2. \(-y^{6}-16y^{5}-64y^{4}\)
3. \(80p^{19}-45p^{5}\)
4. \(192a^{11}+48a^{7}p+3a^{3}p^2\)
5. \(-72a^{5}+50a^{3}\)
6. \(16q^{12}-25q^{4}\)
7. \(80y^{7}-45y^{5}\)
8. \(24p^{12}+120p^{7}s+150p^{2}s^2\)
9. \(245y^{6}-210y^{5}+45y^{4}\)
10. \(-128a^{5}-96a^{4}-18a^{3}\)
11. \(45b^{5}-80b^{3}\)
12. \(180q^{12}-5q^{4}\)

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

Verbetersleutel

1. \(-6p^{4}-36p^{3}-54p^{2}=-6p^{2}(p^2+6p+9)=-6p^{2}(p+3)^2\)
2. \(-y^{6}-16y^{5}-64y^{4}=-y^{4}(y^2+16y+64)=-y^{4}(y+8)^2\)
3. \(80p^{19}-45p^{5}=5p^{5}(16p^{14}-9)=5p^{5}(4p^7+3)(4p^7-3)\)
4. \(192a^{11}+48a^{7}p+3a^{3}p^2=3a^{3}(64a^{8}+16a^4p+p^2)=3a^{3}(8a^4+p)^2\)
5. \(-72a^{5}+50a^{3}=-2a^{3}(36a^{2}-25)=-2a^{3}(6a+5)(6a-5)\)
6. \(16q^{12}-25q^{4}=q^{4}(16q^{8}-25)=q^{4}(4q^4+5)(4q^4-5)\)
7. \(80y^{7}-45y^{5}=5y^{5}(16y^{2}-9)=5y^{5}(4y+3)(4y-3)\)
8. \(24p^{12}+120p^{7}s+150p^{2}s^2=6p^{2}(4p^{10}+20p^5s+25s^2)=6p^{2}(2p^5+5s)^2\)
9. \(245y^{6}-210y^{5}+45y^{4}=5y^{4}(49y^{2}-42y+9)=5y^{4}(7y-3)^2\)
10. \(-128a^{5}-96a^{4}-18a^{3}=-2a^{3}(64a^{2}+48a+9)=-2a^{3}(8a+3)^2\)
11. \(45b^{5}-80b^{3}=5b^{3}(9b^{2}-16)=5b^{3}(3b+4)(3b-4)\)
12. \(180q^{12}-5q^{4}=5q^{4}(36q^{8}-1)=5q^{4}(6q^4+1)(6q^4-1)\)