Ontbinden in factoren (2)

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

1. \(3q^{6}-18q^{5}+27q^{4}\)
2. \(-8p^{6}-8p^{5}-2p^{4}\)
3. \(4s^{7}+4s^{6}+s^{5}\)
4. \(p^{4}+8p^{3}+16p^{2}\)
5. \(108x^{12}-180x^{7}+75x^{2}\)
6. \(-32b^{6}+48b^{5}-18b^{4}\)
7. \(-36s^{9}+25s^{3}\)
8. \(-72q^{7}-24q^{6}-2q^{5}\)
9. \(-147a^{13}+84a^{9}s-12a^{5}s^2\)
10. \(-8y^{6}+2y^{4}\)
11. \(-72a^{17}+50a^{3}\)
12. \(36s^{9}+12s^{7}+s^{5}\)

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

Verbetersleutel

1. \(3q^{6}-18q^{5}+27q^{4}=3q^{4}(q^2-6q+9)=3q^{4}(q-3)^2\)
2. \(-8p^{6}-8p^{5}-2p^{4}=-2p^{4}(4p^{2}+4p+1)=-2p^{4}(2p+1)^2\)
3. \(4s^{7}+4s^{6}+s^{5}=s^{5}(4s^{2}+4s+1)=s^{5}(2s+1)^2\)
4. \(p^{4}+8p^{3}+16p^{2}=p^{2}(p^2+8p+16)=p^{2}(p+4)^2\)
5. \(108x^{12}-180x^{7}+75x^{2}=3x^{2}(36x^{10}-60x^5+25)=3x^{2}(6x^5-5)^2\)
6. \(-32b^{6}+48b^{5}-18b^{4}=-2b^{4}(16b^{2}-24b+9)=-2b^{4}(4b-3)^2\)
7. \(-36s^{9}+25s^{3}=-s^{3}(36s^{6}-25)=-s^{3}(6s^3+5)(6s^3-5)\)
8. \(-72q^{7}-24q^{6}-2q^{5}=-2q^{5}(36q^{2}+12q+1)=-2q^{5}(6q+1)^2\)
9. \(-147a^{13}+84a^{9}s-12a^{5}s^2=-3a^{5}(49a^{8}-28a^4s+4s^2)=-3a^{5}(7a^4-2s)^2\)
10. \(-8y^{6}+2y^{4}=-2y^{4}(4y^{2}-1)=-2y^{4}(2y+1)(2y-1)\)
11. \(-72a^{17}+50a^{3}=-2a^{3}(36a^{14}-25)=-2a^{3}(6a^7+5)(6a^7-5)\)
12. \(36s^{9}+12s^{7}+s^{5}=s^{5}(36s^{4}+12s^2+1)=s^{5}(6s^2+1)^2\)