Ontbinden in factoren (2)

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

1. \(-18b^{19}+2b^{5}\)
2. \(54s^{7}-180s^{5}y+150s^{3}y^2\)
3. \(-36s^{16}+25s^{2}\)
4. \(s^{5}-18s^{4}+81s^{3}\)
5. \(-12q^{4}+75q^{2}\)
6. \(-4b^{7}-4b^{6}-b^{5}\)
7. \(-3q^{6}-12q^{5}-12q^{4}\)
8. \(-245s^{7}+210s^{6}-45s^{5}\)
9. \(s^{7}-s^{5}\)
10. \(-5y^{5}+180y^{3}\)
11. \(-32p^{13}+98p^{3}\)
12. \(12a^{12}+60a^{8}+75a^{4}\)

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

Verbetersleutel

1. \(-18b^{19}+2b^{5}=-2b^{5}(9b^{14}-1)=-2b^{5}(3b^7+1)(3b^7-1)\)
2. \(54s^{7}-180s^{5}y+150s^{3}y^2=6s^{3}(9s^{4}-30s^2y+25y^2)=6s^{3}(3s^2-5y)^2\)
3. \(-36s^{16}+25s^{2}=-s^{2}(36s^{14}-25)=-s^{2}(6s^7+5)(6s^7-5)\)
4. \(s^{5}-18s^{4}+81s^{3}=s^{3}(s^2-18s+81)=s^{3}(s-9)^2\)
5. \(-12q^{4}+75q^{2}=-3q^{2}(4q^{2}-25)=-3q^{2}(2q+5)(2q-5)\)
6. \(-4b^{7}-4b^{6}-b^{5}=-b^{5}(4b^{2}+4b+1)=-b^{5}(2b+1)^2\)
7. \(-3q^{6}-12q^{5}-12q^{4}=-3q^{4}(q^2+4q+4)=-3q^{4}(q+2)^2\)
8. \(-245s^{7}+210s^{6}-45s^{5}=-5s^{5}(49s^{2}-42s+9)=-5s^{5}(7s-3)^2\)
9. \(s^{7}-s^{5}=s^{5}(s^2-1)=s^{5}(s-1)(s+1)\)
10. \(-5y^{5}+180y^{3}=-5y^{3}(y^2-36)=-5y^{3}(y-6)(y+6)\)
11. \(-32p^{13}+98p^{3}=-2p^{3}(16p^{10}-49)=-2p^{3}(4p^5+7)(4p^5-7)\)
12. \(12a^{12}+60a^{8}+75a^{4}=3a^{4}(4a^{8}+20a^4+25)=3a^{4}(2a^4+5)^2\)