Ontbinden in factoren (2)

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

1. \(-128p^{8}-32p^{5}y-2p^{2}y^2\)
2. \(18a^{11}+60a^{7}p+50a^{3}p^2\)
3. \(192a^{11}-336a^{8}q+147a^{5}q^2\)
4. \(4q^{5}-9q^{3}\)
5. \(32p^{6}+48p^{4}+18p^{2}\)
6. \(16y^{11}-y^{5}\)
7. \(-3s^{4}+27s^{2}\)
8. \(20x^{13}-45x^{3}\)
9. \(-48q^{15}-72q^{10}-27q^{5}\)
10. \(-8s^{7}-8s^{6}-2s^{5}\)
11. \(180a^{7}-125a^{5}\)
12. \(y^{5}+6y^{4}+9y^{3}\)

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

Verbetersleutel

1. \(-128p^{8}-32p^{5}y-2p^{2}y^2=-2p^{2}(64p^{6}+16p^3y+y^2)=-2p^{2}(8p^3+y)^2\)
2. \(18a^{11}+60a^{7}p+50a^{3}p^2=2a^{3}(9a^{8}+30a^4p+25p^2)=2a^{3}(3a^4+5p)^2\)
3. \(192a^{11}-336a^{8}q+147a^{5}q^2=3a^{5}(64a^{6}-112a^3q+49q^2)=3a^{5}(8a^3-7q)^2\)
4. \(4q^{5}-9q^{3}=q^{3}(4q^{2}-9)=q^{3}(2q+3)(2q-3)\)
5. \(32p^{6}+48p^{4}+18p^{2}=2p^{2}(16p^{4}+24p^2+9)=2p^{2}(4p^2+3)^2\)
6. \(16y^{11}-y^{5}=y^{5}(16y^{6}-1)=y^{5}(4y^3+1)(4y^3-1)\)
7. \(-3s^{4}+27s^{2}=-3s^{2}(s^2-9)=-3s^{2}(s+3)(s-3)\)
8. \(20x^{13}-45x^{3}=5x^{3}(4x^{10}-9)=5x^{3}(2x^5+3)(2x^5-3)\)
9. \(-48q^{15}-72q^{10}-27q^{5}=-3q^{5}(16q^{10}+24q^5+9)=-3q^{5}(4q^5+3)^2\)
10. \(-8s^{7}-8s^{6}-2s^{5}=-2s^{5}(4s^{2}+4s+1)=-2s^{5}(2s+1)^2\)
11. \(180a^{7}-125a^{5}=5a^{5}(36a^{2}-25)=5a^{5}(6a+5)(6a-5)\)
12. \(y^{5}+6y^{4}+9y^{3}=y^{3}(y^2+6y+9)=y^{3}(y+3)^2\)